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Cyclic Quadrilateral
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Cyclic Quadrilateral
A quadrilateral is called a cyclic quadrilateral if its all vertices lie on a circle.

Theorem: The sum of either pair of apposite angles of a cyclic quadrilateral is 180.
OR
The opposite angles of a cyclic quadrilateral are supplementry.
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Example: In fig, PQRS is a cyclic quadrilateral whose side PQ is a diameter of the circle through P, Q, R, S. If mPSR = 120, find mQPR.
Solution: Since PQRS is a cyclic quadrilateral.
PSR + PQR - 180
120 + PQR = 180
PQR = 60
Since PRQ is the angle in a semi-circle.
PRQ = 90
Now, in PQR, we have
QPR + PRQ + PQR = 180
QPR+ 90+ 60 = 180
QPR = 30
 
   
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