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Mathematics : Circles

Short Answer Type

261. A circle is touching the side BC of ΔABC at P and touching AB and AC produced at Q and R respectively. Prove that

AQ space equals space 1 half space left parenthesis Perimeter space of space increment space ABC right parenthesis

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262. In the given figure, the incircle of ΔABC, touches the sides BC, CA and AB at D, E and F respectively. Show that AF + BD + CE = AE + BF + CD

equals space 1 half left parenthesis perimeter space of space increment space ABC right parenthesis

334 Views

Long Answer Type

263. ABCD is a quadrilateral such that ∠D = 90°. A cirlce C (O, r) touches the sides AB, BC, CD and DA at P, Q, R and S respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm, Find r.

358 Views

Short Answer Type

264. In figure. XP and XQ are tangents from X to the circle with ccentre O. R is a point on the circle. Prove that XA + AR = XB + BR?

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265. In figure a circle touches the side BC of ΔABC at P and touches AB and AC produced at Q and R respectively. If AQ = 5 cm, find the perimeter of ΔABC.

265 Views

Long Answer Type

266. In the given figure, ABC is a right-angled triangle with AB = 6 cm and AC = 8 cm. A circle with centre O has been inscribed inside the triangle. Calculate the value of r, the radius of the inscribed circle.

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Short Answer Type

267.

From a point P outside a circle, with centre O tangents PA and PB are drawn as shown in the figure, prove that

(i) ⇒AOP = ∠BOP
(ii) OP is the perpendicular bisector of AB.

1204 Views

Long Answer Type

268. The radii of two concentric circles are 13 cm and 8 cm. AB is a diameter of the bigger circle. BD is a tangent to the smaller circle touching it at D. Find the length AD.

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Short Answer Type

269. In two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal length.

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270. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle.

625 Views