# NCERT Class 10 Chapter 11 Circles CBSE Board Sample Problems Very Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

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## 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**.

### 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**.

### 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

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 =

## 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

(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.

(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.