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R.D. Sharma solutions 10 Mathematics chapter 10 Circles

Chapter 10 - Circles

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The common point of a tangent to a circle and the circle is called ____

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The common point of a tangent to a circle and the circle is called ____

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A circle can have __________ parallel tangents at the most.

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A circle can have __________ parallel tangents at the most.

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A tangent to a circle intersects it in _______ point (s).

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A tangent to a circle intersects it in _______ point (s).

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A line intersecting a circle in two points is called a __________.

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A line intersecting a circle in two points is called a __________.

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The angle between tangent at a point on a circle and the radius through the point is ........

How many tangents can a circle have?

How many tangents can a circle have?

O is the center of a circle of radius 8cm. The tangent at a point A on the circle cuts a line through O at B such that AB = 15 cm. Find OB

If the tangent at point P to the circle with center O cuts a line through O at Q such that PQ= 24cm and OQ = 25 cm. Find the radius of circle

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If PT is a tangent at T to a circle whose center is O and OP = 17 cm, OT = 8 cm. Find the length of tangent segment PT.

Find the length of a tangent drawn to a circle with radius 5cm, from a point 13 cm from the center of the circle.

A point P is 26 cm away from O of circle and the length PT of the tangent drawn from P to the circle is 10 cm. Find the radius of the circle.

If from any point on the common chord of two intersecting circles, tangents be drawn to circles, prove that they are equal.

If the quadrilateral sides touch the circle prove that sum of pair of opposite sides is equal to the sum of other pair.

If AB, AC, PQ are tangents in Fig. and AB = 5cm find the perimeter of ΔAPQ.

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

In Fig below, PQ is tangent at point R of the circle with center O. If ∠TRQ = 30°. Find
∠PRS.

If PA and PB are tangents from an outside point P. such that PA = 10 cm and ∠APB = 60°. Find the length of chord AB.

From an external point P, tangents PA and PB are drawn to the circle with centre O. If CD is the tangent to the circle at point E and PA = 14 cm. Find the perimeter of ABCD.

In the fig. ABC is right triangle right angled at B such that BC = 6cm and AB = 8cm. Find the radius of its in circle.

From a point P, two tangents PA and PB are drawn to a circle with center O. If OP =
diameter of the circle shows that ΔAPB is equilateral.

Two tangent segments PA and PB are drawn to a circle with center O such that ∠APB =120°. Prove that OP = 2AP

If ΔABC is isosceles with AB = AC and C (0, 2) is the in circle of the ΔABC touching BC at L, prove that L, bisects BC.

In fig. a circle touches all the four sides of quadrilateral ABCD with AB = 6cm, BC = 7cm, CD = 4cm. Find AD.

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

In fig.. O is the center of the circle and BCD is tangent to it at C. Prove that ∠BAC +
∠ACD = 90°

Two circles touch externally at a point P. from a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and E respectively. Prove that TQ = TR.

In the fig. a circle is inscribed in a quadrilateral ABCD in which ∠B = 90° if AD = 23cm,
AB = 29cm and DS = 5cm, find the radius of the circle.

In fig. there are two concentric circles with Centre O of radii 5cm and 3cm. From an
external point P, tangents PA and PB are drawn to these circles if AP = 12cm, find the
tangent length of BP.

In the given figure, AB is a chord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.

In figure PA and PB are tangents from an external point P to the circle with centre O. LN touches the circle at M. Prove that PL + LM = PN + MN

In the given figure, PO  QO. The tangents to the circle at P and Q intersect at a point T. Prove that PQ and OT are right bisector of each other.

In the fig two tangents AB and AC are drawn to a circle O such that ∠BAC = 120°. Prove that OA = 2AB.

In the given figure, BC is a tangent to the circle with centre OOE bisects AP. Prove that ΔAEO~Δ ABC.

The lengths of three consecutive sides of a quadrilateral circumscribing a circle are 4cm,5cm and 7cm respectively. Determine the length of fourth side.

In fig common tangents PQ and RS to two circles intersect at A. Prove that PQ = RS.

In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of (DO')/(CO')

In Fig. 7, two equal circles, with centres O and O’, touch each other at X. OO’ produced meets the circle with centre O’ at A. AC is tangent to the circle with centre O, at the point C. O’D is perpendicular to AC. Find the value of (DO')/(CO')

In figure OQ : PQ = 3 : 4 and perimeter of ΔPDQ = 60cm. determine PQ, QR and OP.

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