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Circles

Short Answer Type

301. TP and TQ are tangents which intersect each other at T. PQ is a chord of length 8 cm and radius is 5 cm. Find the length of TP.

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302. In the given figure, PT and PQ are tangents to a circle with centre at O, touching it at T and Q. If ∠TPQ = 50°, find (i) ∠TBQ (ii) ∠TAQ.

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303. In the given figure, AD is a diameter of a circle with centre at O and AB is a tangent at A. C is a point on the circle such that DC produced interesects the tangent at point B and ∠ABC = 50°. Find ∠AOC.

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304. The radii of two concentric circles are r₁ cm and r₂ cm (r_l > r₂). AB is a diameter of the bigger circle and AP is a tangent to the smaller circle touching the smaller circle at P. Find the length BP.

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305.

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. (Fig. 10.103)

(a) 4 cm (b) 8 cm (c) 3 cm (d) 7 cm

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306.

Two concentric circle are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle. (given in Fig.)

(a) 6 cm (b) 7.5 cm (c) 8 cm (d) 10 cm

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307.

In Fig., If AB = CD = 6 cm then the value of AD + BC is

(a) 10 cm (b) 12 cm (c) 13 cm (d) 14 cm

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308.

In Fig. 10.106, the value of ∠POQ is
(a) 110° (b) 140° (c) 100° (d) 120°

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309.

In Fig. 10.107, If AC = 4 cm, AB = 5 cm and BC = 6 cm then the value of AD is

(a) 7.5 cm (b) 6.5 cm (c) 8.5 cm (d) 9 cm

2AD = AD + AE [ $because$ AD = AE]
= (AC + CD) + (AB + BE)
= (AC + CF) + (AB + BF) = AC + AB + (CF + BF)
= AC + AB + BC = 4 + 5 + 6 = 15 cm
$therefore$ AD = 7.5 cm

Ans. (a)