Question

Prove: The opposite angles of a cyclic quadrilateral are supplementary

PQis a diameter of circle


R is any point on the circle
RS PQ

Prove: SR2 = PS X SQ

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Answer 1

Step-by-step explanation:

Sum of the opposite angles of a cyclic quadrilateral is 180°. But ∠ACB + ∠BAC + ∠ABC = 180° [Sum of the angles of a triangle] ∴ ∠ADC + ∠ABC = 180° ∴ ∠BAD + ∠BCD = 360° – (∠ADC + ∠ABC) = 180°. Hence proved. ... If a pair of opposite angles of a quadrilateral is supplementary, then the quadrilateral is cyclic.