# CBSE Class 10-Mathematics: Chapter –11 Constructions Part 6

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Question 8:

In the given figure, if , prove that .

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

Now

Question 9:

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

Let be two intersection lines.

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

PM = PN [Radii of same circle]

P is equidistance from the lines and

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

P lies on a 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 10:

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

In the given figure,

Also,

is a square

But …(i)