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Circles

Short Answer Type

241. Two tangents TP and TQ are drawn from an external point T to a circle with centre O, as shown in figure, are inclined to each other at angle of 100°, then what is the value of ∠POQ?

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242.

In figure PA and PB are tangents from P to the circle with centre O. R is a point on the circle. Prove that : PC + CR = PD + DR

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243. The length of a tangent from a point A at a distance of 26 cm from the centre of the circles is 10 cm. What will be the radius of the circle?

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244. In figure, 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 cirles.

We know that the perpendicular drawn from the centre of a circle to any chord of the circle, bisects the chord.

So,

OP space perpendicular space AB space rightwards double arrow space AP space equals space PB space equals space square root of OB squared minus OP squared end root equals square root of 25 minus 9 end root equals square root of 16 equals 4

∴ Length of the chord of the larger circle is 2PB = 2 x 4 = 8 cm.

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245. In the figure given below, 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 PB = 12 cm and CQ = 3 cm, what is the length of PC.

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246. The length of the tangent from a point A to circle, of radius 3 cm, is 4 cm. Find the distance of A from the centre of the circle.

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247. In figures, if TP and TQ are two tangents to a circle with centre O so that ∠POQ = 110°, then find ∠PTQ.

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248. In Fig. 10.28, ΔABC is circumscribing a circle. Find the length of BC.

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249. In the following figure, if AD, AE and BC are tangents to the circle at D, E and F respectively, then write 2AD in terms of AB, BC and CA.

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250. In figure, a point P is 13 cm away from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.

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