251.Two tangents TP and TQ are drawn from an external point T to a circle with centre O, as shown in figure. If they are inclined to each other at angle of 70°, then what is the value of ∠POQ?
252.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 = 10 cm and CQ = 2 cm, what is the length of PC?
PA = PB (Tangents from external point P) ⇒ PC + CA = 10 ⇒ PC + CQ = 10 [ ∵ CA = CQ (Tangents from external point C)] ⇒ PC + 2 = 10 ⇒ PC = 8 cm.
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253.The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4 cm. What will be the radius of the circle?
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254.What is the distance between two parallel tangents of a circle of the radius 4 cm?
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255.Two tangents TP and TQ are drawn from an external point T to a circle with centre O, as shown in Fig. If they are inclined to each other at an angle of 100°, then what is the value of ∠POQ?
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256.In figure 2, if ∠ATO = 40°, find ∠AOB.
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257.Two tangents PA and PB are drawn to a cirlce with centre O from an external point P. Prove that ∠APB = 2∠OAB.
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258.O is the centre of two concentric circles of radii 4 cm and 6 cm. PT and PS are tangents to the larger circle and smaller circle respectively from an external point P.PT = 10 cm, find the length of PS.
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259.A circle is inscribed in a ΔABC, having sides 8 cm, 10 cm, and 12 cm, as shown in Fig. Find AD, BE and CF.
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260.In figure, a circle touches all the four sides of a quadrilateral ABCD/ whose sides AB = 6 cm, BC = 7 cm and CD = 4 cm. Find AD.
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