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Circles

Short Answer Type

291. The length of tangent from a point A at a distance of 14 cm from the centre of the circle is 11 cm. What will be radius of the circle?

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292. If figure if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 120°,. then what is the value of ∠PTQ?

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293. Two tangents TP and TQ are drawn from an external point T to a circle with centre O, as shown in figure, If they are inclined to each other at an angle of 110°, then what is the value of ∠POQ?

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294. In the figure belwo, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PA = 10 cm and DQ = 2 cm, what the length of PC?

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295. In the given figure, a circle is inscribed in a quadrilateral ABCD. If BC = 30 cm, BP = 22 cm, CD = 30 cm and AD ⊥ CD, find the radius of the circle.

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296. ABC is a right-angled triangle with AB = 16 cm, BC = 12 cm and AC = 20 cm. A circle with centre at O and radius r is inscribed in ΔABC. Find the value of r.

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297. In the given figure, PA and PB are tangents to a circle from an external point P touching the circle at A and B. QR is a tangent at a point S, intersecting PA and PB at Q and R respectively. Find the perimeter of ΔPQR if PA= 8 cm.