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.
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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.
248.In Fig. 10.28, ΔABC is circumscribing a circle. Find the length of BC.
∴ Tangents drawn from an external point of a circle are equal ∴ BP = BR = 3 cm AQ = AR = 4 cm PC = CQ = AC – AQ = 11 cm – 4 cm = 7cm Now, BC = BP + PC = 3 cm + 7 cm = 10 cm
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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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