Question
Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
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Text solutionVerified
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 Type | Text solution:1 |
Upvotes | 151 |