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### High School Mathematics - 28.3 Cyclic Quadrilateral

 Cyclic Quadrilateral: A quadrilateral whose vertices lie on the circumference of a circle is called cyclic quadrilateral. Theorem: Opposite angles of a cyclic quadrilateral are supplementary. Proof: Directions: Solve the following.
 Q 1: Prove that the exterior angle of a cyclic quadrilateral is equal to its interior opposite angle.Answer: Q 2: Prove that when a parallelogram is inscribed in a circle it becomes a rectangleAnswer: Q 3: A pair of opposite sides of a cyclic quadrilateral is equal. Prove that their diagonals are equal.Answer: Q 4: PQRS is a cyclic quadrilateral whose diagonals intersect at A.If ang SQR = 80o, angle QPR = 30o, find angle SRQ.90o80o70o Q 5: PQRS is a cyclic quadrilateral, if angleQ = angleR = 65o, find angle P and angle S.120o115o100o Q 6: Answer: Q 7: Answer: Q 8: Answer: Question 9: This question is available to subscribers only! Question 10: This question is available to subscribers only!

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