CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 18
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Question 20:
In the given figure, if , prove that .

Tangents from an Exterior
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.

Find the Locus of Centre of Circle
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)