# CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 13 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 3**:

Two tangents TP and TQ are drawn from an external point T with center O as shown in figure. If they are inclined to each other at an angle of , then what is the value of

**Answer**:

and TQ are tangents and O is the center of the circle

**Question 4**:

Two concentric circles are of radii and , find the length of the chord of the larger circle which touches the smaller circle.

**Answer**:

is the chord of the larger circle which touches the smaller circle at the point L. Since is tangent at the point L to the smaller circle with centre .

is a chord of the bigger circle and

In

Chord

Length of chord

**Question 5**:

A quadrilateral ABCD is drawn to circumscribe a circle. Prove that .

**Answer**:

AP, AS are tangents from a point A (Outside the circle) to the circle.

Similarly,

Now

**Question 6**:

PQ is a chord of length of a circle of radius . The tangents at P and Q intersect at point T. Find the length TP.

**Answer**:

Join OT.

[tangents from T upon the circle]

And bisects PQ

Now

Now