Circles ncert solutions Chapter 10 Exercise 10.2 Question 13
13. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
Solution:
Given: ABCD is a quadrilateral and it circumscribes a circle. Let O be the center of the circle.
To Prove:
Proof:
In
and
OP = OQ {Radius of circle}
OA = OA (Common side}
AP = AQ {Tangents drawn from an external point to the circle are equal}
Therefore, by SSS congruence axiom,
Therefore,
{Corresponding angles of congruent triangles are equal} (1)
Similarly,
(2)
And,
(3)
And,
(4)
We also have,
Using equations (1), (2), (3) and (4) in the above equation, we can say that
Hence proved
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