CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 18 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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)