# CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 8 (For CBSE, ICSE, IAS, NET, NRA 2023)

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**Question 14**:

In the given figure, O is the center of the circle with radius 5 cm and AB|| CD. If AB = 6 cm, find OP.

**Answer**:

From right

**Question 15**:

Prove that the tangents at the end of a chord of a circle make equal angles with the chord.

**Answer**:

In and

And

[Common]

**Question 16**:

Find the locus of the center of circles which touch a given line at a given point.

**Answer**:

Let APB be the given line and let a circle with center touch APB at P. Then , let there be another circle with center O ′ which touches the line APB at P.

Thus,

**Question 17**:

In the given figure, find the perimeter of , if .

**Answer**:

BC touches the circle at R

Tangents drawn from external point to the circle are equal.

And

Perimeter of

**Question 18**:

**I**f PA and PB are tangents drawn from external point P such that and , find the length of chord AB.

**Answer**:

is equilateral triangle