# CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 12 (For CBSE, ICSE, IAS, NET, NRA 2022)

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**Question 34**:

In the given figure, if TP and TQ are the two tangents to a circle with center O so that , then find .

**Answer**:

Since

**Question 35**:

In the figure, given below PA and PB are tangents to the circle drawn from an external point P. CD is the third tangent touching the circle at Q. If and , what is the length of ?

**Answer**:

## 3 Mark Questions

**Question 1**:

Prove that the angel between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line-segment joining the points of contact at the center.

**Answer**:

[Tangent at any point of a circle is to the radius through the point of contact]

OAPB is quadrilateral.

[Angle sum property of a quadrilateral]

are supplementary.

**Question 2**:

Prove that the parallelogram circumscribing a circle is a rhombus.

**Answer**:

Given: ABCD is a parallelogram circumscribing a circle.

To Prove: ABCD is a rhombus.

**Proof**: Since the tangents from an external point to a circle are equal.

… (i)

… (ii)

… (iii)

… (iv)

On adding eq. (i) , (ii) , (iii) and (iv) , we get

But and [Opposite sides of ]

Parallelogram ABCD is a rhombus.