Exercise 10.2
In Q.1 to 3, choose the correct option and give justification.
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
Solution:
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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 ∠POQ
= 110°, then ∠PTQ is equal to
(A) 60° (B) 70° (C) 80° (D) 90°
Solution:
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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 POA is equal to
(A) 50° (B) 60° (C) 70° (D) 80°
Solution:
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Question 4: Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
Solution:
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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.
Solution:
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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.
Solution:
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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.
Solution:
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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
Solution:
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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 ∠AOB = 90°.
Solution:
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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.
Solution:
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Question 11: Prove that the parallelogram circumscribing a
circle is a rhombus.
Solution:
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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.
Solution:
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Question 13: Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle. F
Solution: