# CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 18

Get top class preparation for CBSE right from your home: fully solved questions with step-by-step explanation- practice your way to success.

**Question 20:**

In the given figure, if , prove that .

**Answer:**

Since tangents from an exterior point A to a circle are equal in length

Similarly, tangents from an exterior point B to a circle are equal in length

Similarly, for

…………. (3)

Now

**Question 21:**

Find the locus of center of circle with two intersecting lines.

**Answer:**

Let be two intersection lines.

Let a circle with center P touch the two lines and at M and N respectively.

[Radii of same circle]

P is equidistance from the lines

Similarly, center of any other circle which touch the two intersecting lines will be equidistant from and

P lies on bisector of the angle between and

[The locus of points equidistant from two intersecting lines is the pair of bisectors of the angle between the lines]

Hence, locus of center of circles which touch two intersecting lines is the pair of bisectors of the angles between the two lines.

**Question 22:**

In the given figure, a circle is inscribed in a quadrilateral ABCD in which . If and , find the radius of the circle.

**Answer:**

In the given figure, and

Also,

is a square

But …(i)