Telangana SCERT Solution Class X (10) Maths Chapter 9 Tangents and Secants to a circle Exercise 9.2
Choose the correct answer and give justification for each.
(i) The angle between a tangent to a circle and the radius drawn at the point of contact is
(a) 60° (b) 30° (c) 45° (d) 90°
(ii) From a point Q, the length of the tangent to a circle is 24 cm. and the distance of Q from the centre is 25 cm. The radius of the circle is
(a) 7cm (b) 12 cm (c) 15cm (d) 24.5cm
(iii) If AP and AQ are the two tangents a circle with centre O so that Ð =° QOP 110 , then ÐPAQ is equal to
(a) 60° (b) 70° (c) 80° (d) 90°
(iv) If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of 80°, then ÐPOA is equal to
(a) 50° (b) 60° (c) 70° (d) 80°
(v) In the figure, XY and X1Y 1 are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X1Y 1 at B then Ð = BOA
(a) 80° (b) 100° (c) 90° (d) 60°
Q2> Two concentric circles of radii 5 cm and 3cm are drawn. Find the length of the chord of the larger circle which touches the smaller circle.
Q3. Prove that the parallelogram circumscribing a circle is a rhombus.
Q4> . A triangle ABC is drawn to circumscribe a circle of radius 3 cm. such that the segments BD and DC into which BC is divided by the point of contact D are of length 9 cm. and 3 cm. respectively (See adjacent figure). Find the sides AB and AC.
Given that,
BD = 9cm and CD= 3 cm
Radius of the circle OD = 3cm
we know that,
The lengths of tangents drawn from an external point are equal
BD = BF = 9cm
CD = CE = 3cm
Q5> Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths. Verify by using Pythogoras Theorem.
Q6> Construct a tangent to a circle of radius 4cm from a point on the concentric circle of radius 6cm and measure its length. Also verify the measurement by actual calculation.
Q7> Draw a circle with the help of a bangle. Take a point outside the circle. Construct the pair of tangents from this point to the circle and measure them. Write your conclusion.
Q8> In a right triangle ABC, a circle with a side AB as diameter is drawn to intersect the hypotenuse AC in P. Prove that the tangent to the circle at P bisects the side BC.
Q9> Draw a tangent to a given circle with center O from a point ‘R’ outside the circle. How many tangents can be drawn to the circle from that point?
Here is your solution of Telangana SCERT Class 10 Math Chapter 9 Tangents and Secants to a circle Exercise 9.2
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