NCERT class 10 maths chapter 10 Circles
Question 1: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) 7 cm (B) 12 cm (C) 15 cm (D) 24.5 cm
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Question 2:In Fig. 10.11, if TP and TQ are the two tangents to a circle with centre O so that Ð POQ = 110°, then Ð PTQ is equal to (A) 60° (B) 70° (C) 80° (D) 90°
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Question 3: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 Ð POA is equal to (A) 50° (B) 60° (C) 70° (D) 80°
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Question 4:Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
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Question 5:Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre.
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Question 6:The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.
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Question 7:Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.
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Question 8:A quadrilateral ABCD is drawn to circumscribe a circle (see Fig. 10.12). Prove that AB + CD = AD + BC Fig. 10.12 Fig. 10.13
EXERCISE 10.2In Q.1 to 3, choose the correct optio
Question 9:In Fig. 10.13, XY and X¢Y¢ are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting XY at A and X¢Y¢ at B. Prove that Ð AOB = 90°.
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Question 10:Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the centre.
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Question 11:Prove that the parallelogram circumscribing a circle is a rhombus.
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Question 12:A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig. 10.14). Find the sides AB and AC.
Question 13:Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.