RS Aggarwal Class 6 Math Eighteenth Chapter Circles Exercise 18 Solution

EXERCISE 18

CIRCLEA circle is the collection of all those points in a plane whose distance from a fixed point remains constant.

INTERIOR CIRCLEThe part of the plane, consisting of those points which are less than the radius of the circle is called the interior of the circle.

EXTERIOR CIRCLEThe part of the plane, consisting of those points which are greater than the radius of the circle is called the exterior of the circle.

DIAMETER OF A CIRCLEA line segment passing through the centre of a circle and having its end points on the circle is called a diameter of the circle.

CHORD OF A CIRCLEA line segment with its end points lying on a circle is called a chord of the circle.

SECANT OF A CIRCLEA line passing through a circle and intersecting the circle at two points is called a secant of the circle.

CIRCUMFERENCE OF A CIRCLEThe perimeter of a circle is called circumference.

SEGMENTS OF A CIRCLEA chord of a circle divides the circular region into two parts. Each part is called segment of the circle.

SEMICIRCLEThe end points of a diameter of a circle divide the circle into two equal parts; each part is called a semicircle.

ARC Any part of a circle is called arc of a circle.

SECTOR OA A CIRCLEThe area bounded by an arc and the two radii joining the end points of the arc with the centre is called a sector.

CONCENTRIC CIRCLESTwo or more circles with the same centre are called concentric circle.

(1) Take a point O on your notebook and draw circles of radii 4cm, 5.3 cm and 6.2 cm, each having the same centre O.

This is the required diagram.

(2) Draw a circle with centre C and radius 4.5 cm. Mark points P, Q, R such that P lies in the interior of the circle, Q lies on the circle, and R lies in the exterior of the circle.

This is the required diagram.

(3) Draw a circle with centre O and radius 4 cm. Draw a chord AB of the circle. Indicate by marking points X and Y, the minor arc AXB and the major arc AYB of the circle.

This is the required diagram.

(4) Which of the following statements are true and false?

(i) Each radius of a circle is also a chord of the circle. = False

(ii) Each diameter of a circle is also a chord of the circle. = True

(iii) The center of a circle bisects each chord of the circle. = False

(iv) A secant of a circle is a segment having its end points on the circle. = False

(v) A chord of a circle is a segment having its end points on the circle. = True

(5) Draw a circle with centre O and radius 3.7 cm. Draw a sector having the angle 72o.

Therefore, the required arc is arc OACB.

(6) fill in the blanks by using <, >, = or .

(i) OP > OQ, where O is centre of the circle, P lies on the circle and Q is in the interior of the circle.

(ii) OP < OR, where O is the center of the circle, P lies on the circle and R lies in the exterior of the circle.

(iii) Major arc > minor arc of the circle.

(iv) Major arc > semi circumference of the circle.

(7) Fill in the blanks:

(i) A diameter of a circle is a chord that passes through the centre.

(ii) A radius of a circle is a line segment with one end point at the centre and the other end point on the circle.

(iii) If we join any two points of a circle by a line segment, we obtain a chord of the circle.

(iv) Any part of a circle is called an arc of the circle.

(v) The figure bounded by an arc the two radii joining the end points of the arc with the centre is called a sector of the circle.

Updated: May 30, 2022 — 12:43 pm