# CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 11

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**Question 29:**

In the given figure, ABCD is a cyclic quadrilateral and PQ is a tangent to the circle at C. If BD is a diameter, and , find .

**Answer:**

is a diameter

[Angle in the semi-circle]

**Question 30:**

Two chords AB and CD of a circle intersect each other at P outside the circle. If cm, and , find .

**Answer:**

[length of tangent from P]

**Question 31:**

In the adjoining figure, if AD, AE, and BC are tangents to the circle at D, E and F respectively, then prove that .

**Answer:**

Now

**Question 32:**

In figure, PA and PB are tangents from P to the circle with center O. R is a point on the circle, prove that .

**Answer:**

Since length of tangents from an external point to a circle are equal in length

And

Now

**Question 33:**

The length of tangents from a point A at distance of from the centre of the circle is , what will be the radius of the circle?

**Answer:**

Since tangents to a circle is perpendicular to radius through the point of contact

In right , we have