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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.

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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.

Since tangent to a circle is always, perpendicular to the radius through the point of contact.

∴ ∠OTA = 90°
In right triangle OTA, we have
OA² = OT² + AT²⇒ OA² = (3)² + (4)² = 9 + 16 = 25
⇒ OA = 5

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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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