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# RD Sharma solutions for Class 10th Board Exam Mathematics chapter 10 - Circles

## Chapter 10 : Circles

#### Page 5

Q 1.1 | Page 5

Fill in the blank:

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

Q 1.1 | Page 5

Fill in the blank:

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

Q 1.2 | Page 5

Fill in the blank:

A circle can have __________ parallel tangents at the most.

Q 1.2 | Page 5

Fill in the blank:

A circle can have __________ parallel tangents at the most.

Q 1.3 | Page 5

Fill in the blank:

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

Q 1.3 | Page 5

Fill in the blank:

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

Q 1.4 | Page 5

Fill in the blank:

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

Q 1.4 | Page 5

Fill in the blank:

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

Q 1.5 | Page 5

Fill in the blank

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

Q 2 | Page 5

How many tangents can a circle have?

Q 2 | Page 5

How many tangents can a circle have?

Q 3 | Page 5

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

Q 4 | Page 5

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

#### Pages 33 - 37

Q 1 | Page 33

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.

Q 2 | Page 33

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

Q 3 | Page 33

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.

Q 4 | Page 33

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

Q 5 | Page 33

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

Q 6 | Page 33

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

Q 7 | Page 33

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

Q 8 | Page 33

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

Q 9 | Page 33

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.

Q 10 | Page 34

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.

Q 11 | Page 34

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.

Q 12 | Page 34

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.

Q 13 | Page 34

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

Q 14 | Page 34

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.

Q 15 | Page 34

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

Q 16 | Page 35

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

Q 16 | Page 35

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

Q 17 | Page 35

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

Q 18 | Page 35

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.

Q 19 | Page 35

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.

Q 20 | Page 35

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.

Q 21 | Page 35

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.

Q 22 | Page 35

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

Q 23 | Page 35

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.

Q 24 | Page 35

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

Q 25 | Page 36

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

Q 26 | Page 36

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

Q 27 | Page 36

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

Q 28 | Page 37

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')

Q 28 | Page 37

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')

Q 29 | Page 37

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

## RD Sharma solutions for Class 10th Board Exam Mathematics chapter 10 - Circles

RD Sharma solutions for Class 10th Board Exam Maths chapter 10 (Circles) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE 10 Mathematics solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 10th Board Exam Mathematics chapter 10 Circles are Theorem of External Division of Chords, Theorem of Internal Division of Chords, Converse of Theorem of the Angle Between Tangent and Secant, Theorem of Angle Between Tangent and Secant, Converse of Cyclic Quadrilateral Theorem, Corollary of Cyclic Quadrilateral Theorem, Theorem of Cyclic Quadrilateral, Corollaries of Inscribed Angle Theorem, Inscribed Angle Theorem, Intercepted Arc, Inscribed Angle, Property of Sum of Measures of Arcs, Tangent Segment Theorem, Converse of Tangent Theorem, Circles passing through one, two, three points, Tangent Properties - If Two Circles Touch, the Point of Contact Lies on the Straight Line Joining Their Centers, Cyclic Properties, Tangent - Secant Theorem, Cyclic Quadrilateral, Angle Subtended by the Arc to the Point on the Circle, Angle Subtended by the Arc to the Centre, Introduction to an Arc, Touching Circles, Number of Tangents from a Point on a Circle, Tangent to a Circle, Tangents and Its Properties, Theorem - Converse of Tangent at Any Point to the Circle is Perpendicular to the Radius, Number of Tangents from a Point to a Circle, Tangent to a Circle, Number of Tangents from a Point on a Circle, Circles Examples and Solutions, Introduction to Circles.

Using RD Sharma Class 10th Board Exam solutions Circles exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 10th Board Exam prefer RD Sharma Textbook Solutions to score more in exam.

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