# CBSE Class 10-Mathematics: Questions and Answers Chapter –10 Circles Part 6

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Question 6:

If tangents PA and PB from a point P to a circle with center are inclined to each other at angle of , then is equal to:

(A)

(B)

(C)

(D)

(A)

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

[Centre lies on the bisector of the angle between the two tangents]

In ,

[Angle sum property of a triangle]

Question 7:

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Given: PQ is a diameter of a circle with center O.

The lines AB and CD are the tangents at P and Q, respectively.

To Prove:

Proof: Since AB is a tangent to the circle at P and OP is the radius through the point of contact.

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

CD is a tangent to the circle at Q and OQ is the radius through the point of contact.

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

From eq. (i) and (ii),

But these form a pair of equal alternate angles also,

Question 8:

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center.