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Question

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angle at the center of the circle.

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Solution

Data : Circle withe centre 'O' is circumscribed in a quadrilateral ABCD
To Prove : AOD+BOC=180
Sides of the quadrilateral AB , BC , CD and DA touches at the points P, Q , R and S respectively
OA . OB , OC , OD and OP , OQ , OR , OS are joined OA bisects POS
1=2
3=4
5=6
7=8
2(1+4+5+8)=360
(1+8)(4+5=180
AOD=BOD=180
opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
1956260_1867368_ans_ef753803e8e24acfbf04e9fdc9af3278.png

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