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Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

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Let be the quadrilateral circumscribing a circle at the center 
such that it touches the circle at the point . Let join the vertices of the quadrilateral to the center of the circle

In and

( Tangents from to same point )

( Radii of the same circle)

( Common side)

so,   (SSS congruence criterion)

(CPCT)

Similarly





()







Similarly we can prove
Hence proved.
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Question Text
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
Answer TypeText solution:1
Upvotes151