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Circles

Short Answer Type

281. The length of tangent from a point A at distance 7 cm from the centre is

2 square root of 6 space cm

. What will be the radius of the circle?

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282. In figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 105°, then what is the value of ∠PTQ?

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283. In the given figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, find AB + BC + CA in terms of AD.

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284. If tangents PA and PB from a point P to a circle with a cenre O are inclined to each other at an angle of 70°, then what is the value of the ∠POA?

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285.

From a point A, the length of the tangent to a circle is $bold 6 square root of bold 5$ cm and the distance of A from thecentre is 18 cm. Find the radius of the circle.

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286. If tangents PA and PB from a point P to a circle with centre O are inclined to each othe at an angle of 80°, then what is the value of ∠POA?

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287. In figure, a circle touches all the four sides of a quadrilateral ABCD with AB = 6 cm, BC = 7 cm and CD = 4 cm. What is length of AD?

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288. Find the length of a tangent to a circle with radius 8 cm from a point 17 cm from the centre of the circle.

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289. If tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of 60°, then what is the value of ∠POA?

Solution not provided.

Ans. 60°

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290. In the figure given below, PQ and PR are tangents to the circle drawn from an external point P, LM is a third tangent touching the circle at K, If PQ = 15 cm, KM = 4 cm, find the length PL.

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