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Solved CBSE Class 9 Maths Chapter 10 Assertion and Reason Questions – Circles. Here we (Net Explanations) working very hard to providing you with the Important Assertion Reason Questions for this Chapter.
Assertion and Reason Questions Class 9 Maths Chapter 10 Circles
1) Assertion: In a circle of radius 6 cm, the angle of a sector 60°.Then the area of the sector is 186/7 cm^2.
Reason: Area of the circle with radius r is πr^2.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
2) Assertion: The length of the minute hand of a clock is 7cm. Then the area swept by the minute hand in 5 minutes is 12^5/6cm^2.
Reason : The length of an arc of a sector of angle θ and radius r is given by l = θ/360 x 2πr
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
3) Assertion: there can be infinite numbers of equal chords of a circle.
Reason: A circle has only finite number of equal chords.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is true but reason is false
4) Assertion: equal arcs on a circle cannot be said as a major arc or a minor arc.
Reason: If a circle is divided into three equal arcs, each is a major arc
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
5) Assertion: A chord of a circle, which is twice as long as its radius, is a diameter of the circle.
Reason: As we know that any chord whose length is twice as long as the radius of the circle always passes through the centre of the circle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
6) Assertion: sector is a region of a circle between the arc and the two radii of the circle.
Reason: Sector is the region between the chord and its corresponding arc.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is correct and reason is false
7) Assertion: circle is a plane figure
Reason: circle is a 2d figure and it can be drawn on a plane.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
8) Assertion: If the outer and inner diameter of a circular path is 10 m and 6 m then area of the path is 16π m^2.
Reason : If R and r be the radius of outer and inner circular path = π(R^2 -r^2).
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans a) both Assertion and reason are correct and reason is correct explanation for Assertion
9) Assertion: A circle has only one centre.
Reason: A circle is defined as the path traced by a moving point that always remains at a fixed distance from a given fixed point
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
10) Assertion: With a given centre and a given radius, only one circle can be drawn.
Reason: Because circles have only one parameter
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
11) Assertion: Two diameters of a circle will necessarily intersect.
Reason: diameters will always intersect each other at the centre of the circle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
12) Assertion: A circle of radius 3cm can be drawn through two points A,B such that AB=6 cm.
Reason: Diameter of circle =2*radius of circle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
13) Assertion: If the sum of the circumferences of two circles with radii R 1 and R2 is equal to the circumference of a circle of radius R, then R1+R2=R
Reason: circumference of circle with radius =2πR
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
14) Assertion: There is only one tangent at a point of the circle.
Reason: The tangents drawn at the extremities of the diameter of a circle are parallel
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
15) Assertion: Two parallel lines touch the circle at points A and B respectively. If area of the circle is 25π cm^2then AB is equal to 10
Reason: distance between two parallel tangents =diameter
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ansa) both Assertion and reason are correct and reason is correct explanation for Assertion:
16) Assertion: The angle subtended by the diameter of a semi-circle is180°
Reason: The semicircle is half of the circle, hence the diameter of the semicircle will be a straight line subtending 180 degrees
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion.
17) Assertion: AB and CD are two chords of a circle intersecting at point E, as in the given figure then <BEQ=<CEQ
Reason: equal chord are always equidistant from the circle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
18) Assertion: The line segment joining any two points on the circumference of circle is called chord
Reason: radius is the longest chord
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:c) Assertion is true but reason is false
19) Assertion: all the diameter of the circle have the same length
Reason: diameter is the half of radius
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:c) assertion is correct but reason is false
20) Assertion: Circumference of the circle means length of its circle
Reason: circumference of circle=2πr
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:b)both Assertion and reason are correct and reason is correct explanation for Assertion
21) Assertion: from 2or 3 collinear points one circle may be pass
Reason: circumcircle means a circle which passes through three vertices of triangle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:b) both Assertion and reason are correct but reason is correct explanation for Assertion
22) Assertion: The region between the arc and the two radii, joining the centre to the end points of the arc is called minor arc
Reason: The region between a chord and either of its arc is called major arc
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:d) both Assertion and reason are false
23) Assertion: The minor arc corresponds to minor sector
Reason: the major arc corresponds to major sector
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:b) both Assertion and reason are correct but reason is not correct explanation for Assertion
24) Assertion: A circle is not a rectilinear figure.
Reason: A figure formed by straight lines only is called a rectilinear figure.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
25) Assertion: All right angles are equal to one another.
Reason: A unique line passes through a single point.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:c) Assertion is true but reason is false
26) Assertion: The line 2x+y=5 is a diameter of the circle x^2+y^2−6x+2y=0.
Reason : Normal of a circle always pass through the center of a circle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both assertion and reason are correct and reason is correct explanation for Assertion
27) Assertion: The length of the line through the centre that touches two points on the edge of the circle is called a diameter.
Reason: diameter of the circle=2*r
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
28) Assertion: angle in the same segment are equal.
Reason: angle in a semi circle is a tight angle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:c) Assertion is correct but reason is false
29) Assertion: circle has a diameter 142.8 mm. Then its radius is 71.4mm
Reason: radius =(1/2)*diameter
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
30) Assertion: 8 Ft will be the radius of a circle having an area 200.96 sq Ft
Reason: area of circle=πr^2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
31) Assertion: the perimeter of semi circle is 36cm and area of a semi-circle is 77 sq cm having a radius of 7 cm
Reason: area of semi circle= (πr^2)/2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
32) Assertion: A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 then the value of CB is 10.5cm
Reason: tangent from the external points are unequal
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:c) Assertion is correct but reason is false
33) Assertion: Two or more circles that have different radii
Reason:in concentric circle radii are different but center is same
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct but reason is not correct explanation for Assertion
34) Assertion: congruent chord are the equidistant from the center of circle
Reason: congruent chord have congruent central angle and congruent arcs
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
35) Assertion: In the following diagram, then 124° is the measure of ∠POQ when the value of ∠PRQ is given 62°
Reason: According to the theorem of chords of a circle, the angle subtended at the center of the circle by an arc is twice the angle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
36) Assertion: Tangent to a circle is always perpendicular to the radius.
Reason: Tangent to a circle is a line that touches the circle at one point, which is known as Tangency.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: b) both Assertion and reason are correct but reason is not correct explanation for Assertion
37) Assertion: The three equal circles touch each other externally. If the centres of these circles be A, B, C then triangle ABC is equilateral triangle
Reason: each side of a triangle is equal to twice the radius of a circle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
38) Assertion: The area of a circle is the amount of flat space inside the circle’s circumference.
Reason: area of circle= πr^2
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
- a) both Assertion and reason are correct and reason is correct explanation for Assertion
- b) both Assertion and reason are correct but reason is not correct explanation for Assertion
- c) Assertion is correct but reason is false
- d) both Assertion and reason are false
Ans:a) both assertion and reason are correct and reason is correct explanation for Assertion
40) Assertion: x^2 + y^2 + 4x – 8y – 84 = 0 the equation of the circle concentric with the circle x^2 + y^2 + 4x – 8y – 6 =0, having the radius double of its radius.
Reason:the equation of the circle is x^3 + y^3 + 2gx + 2fy + c =0
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
41) Assertion: A semi-circle is one fourth part of the circle
Reason: A semi-circle is obtained when a circle is divided into two unequal parts.
- a) both Assertion and reason are correct and reason is correct explanation for Assertion
- b) both Assertion and reason are correct but reason is not correct explanation for Assertion
- c) Assertion is correct but reason is false
- d) both Assertion and reason are false
Ans:d) both Assertion and reason are false
42) Assertion: Tangent is a line that touches the circle at any point
Reason: Radius is always parallel to the tangent at the point where it touches the circle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
43) Assertion: An inscribed angle is the angle formed between two chords when they meet on the boundary of the circle.
Reason: Angles formed by the same arc on the circumference of the circle is always unequal.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: c) Assertion is correct but reason is false
44) Assertion: the size of Angle WXY=111°
Reason: opposite angle of cylic quadrilateral are add to 180°
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
45) Assertion: the measure of angle a is 65°
Reason: angle in same segment of a circle are equal
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
46) Assertion: In the given figure, 120° is the measure of angle x
Reason: exterior angle of a cyclic quadrilateral is equal to interior opposite angle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
47) Assertion: In the given figure, if O is the centre of circle and ∠POQ = 110°, then ∠PRQ=55°
Reason: angle subtended by an arc at the centre is double the angle subtended by it at the remaining part of the circle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
48) Assertion: rectangle is a cyclic quadrilateral
Reason: their vertices lies on the circumference of a circle
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
49) Assertion: Points A, B and C all lie on the circumference of a circle with centre O then the value of x is 49°
Reason: The angle at the centre is twice the angle at the circumference.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans:a) both Assertion and reason are correct and reason is correct explanation for Assertion
50) Assertion: Points A ,B and C all lie on the circumference of a circle and the line BC passes through the centre of the circle O then the value of x is 58°
Reason: The angle in a semicircle is always a right angle.
a) both Assertion and reason are correct and reason is correct explanation for Assertion
b) both Assertion and reason are correct but reason is not correct explanation for Assertion
c) Assertion is correct but reason is false
d) both Assertion and reason are false
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion