CBSE Class 10-Mathematics: Questions and Answers Chapter – 10 Circles Part 14
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Question 7:
A circle is touching the side BC of at P and touching AB and AC produced at Q and R, respectively. Prove that (perimeter of ).

The Two Tangents Drawn to a Circle
Answer:
We know that the two tangents drawn to a circle from an external point are equal.
Perimeter of
Question 8:
If PA and PB are two tangents drawn from a point P to a circle with center O touching it at A and B. Prove that OP is the perpendicular bisector of AB.

Point P to a Circle with Centre O
Answer:
Let intersect AB at a point C, we have to prove that and
are two tangents from a point P to the circle with center
In two ACP and BCP, we have
[tangents from P to the circle are equal]
[Common]
And
But
Hence, is perpendicular bisector of .
Question 9:
In the given figure, PQ is tangent at point R of the circle with center O. If , find .

Given PQ is Tangent at Point R
Answer:
Given is tangent at point R and
[Tangent of a circle is perpendicular to Radius]
Question 10:
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.

Prove That Opposite Sides of a Quadrilateral
Answer:
Let the circle touch the sides AB, BC, CD and DA at the points P, Q, R, and S, respectively.
Join OP, OQ, OR and OS.
Join OA, OB, OC, and OD.
Since the two tangents drawn from an external point subtend equal angles at the center.
But
And
And