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Circles

Short Answer Type

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?

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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?

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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.

Since, length of two tangents drawn from an external point of circle are equal.
So,    AP = AS
BP = BQ DR = DS
and    RC = CQ
Adding all, we get
(AP + BP) + (DR + RC) = AS + BQ + DS + CQ
⇒ (AP + BP) + (DR + RC)
= (AS + DS) + (BQ + CQ)
⇒    AB + DC = AD + BC
⇒    6 + 4 = AD + 7
⇒    10 = AD + 7
AD = 10 – 7 = 3 cm
Hence, AD = 3 cm.

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Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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.

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.