NCERT Class 10 Chapter 11 Circles CBSE Board Sample Problems Very Short Answer (For CBSE, ICSE, IAS, NET, NRA 2022)

Doorsteptutor material for CBSE/Class-10 is prepared by world's top subject experts: get questions, notes, tests, video lectures and more- for all subjects of CBSE/Class-10.

Question

In the given fig. AP and BP are tangents to circle with center o, such that AP = 5 cm and, . Find the length of chord AB.

Circle with Center O

Solution

In

(Tangents from an external point P)

Let

Then in

As all three angles of are 60. So is an equilateral triangle

. Hence

Question

In the given figure. Two circles touch each other at point C. prove that the common tangent to the circles at C, bisects the common tangent at P and Q.

Two Circles Touch Each Other at Point C

Solution

PR and RC are tangents to circle with center A.

(Tangents from common point R) … 1

Similarly, RQ and RC are tangents to circle with center B.

From 1 and 2, CR bisects PQ

Question

A tangent PQ at a point P of a circle of radius 5 cm meets a line a through the center O at a point Q so that OQ = 13 cm. Find the length PQ.

Solution

Acircle of Radius

Given,

Now, in triangle

(Radius is perpendicular to tangent at point of contact)

Question

Two circles are of radii a and are given. Find the length of the chord of the larger circle which touches the smaller circle.

Solution

AB is a tangent at C to a circle

(Perpendicular from center to chord bisects the chord)

Now in triangle OCA,

Length of chord =

Two Circles

Question

In two concentric circles, a chord of length 24 cm of larger circle becomes a tangent to the smaller circle whose radius is 5 cm. Find the radius of the larger circle.

Solution

Two Concentric Circles

(Perpendicular from the bisects the chord

Hence

Question

In an isosceles triangle and if in circle of triangle ABC touches BC at L. Show

L bisects BC.

Solution

Given: If is isosceles with AB = AC and C (O, r)

is the in circle of the touching BC at L.

To prove: L bisect BC.

Proof:

Construct the figure according to given condition.

Isosceles Triangle

(Given)

(Length of tangents dawn from an external point to a circle are equal)

Since,

(Length of tangents dawn from an external point to a circle are equal) (ii)

(Length of tangents dawn from an external point to a circle are equal) (iii)

From equation i, ii and iii

Hence. L bisects BC.

Developed by: