Cyclic Quadrilaterals – Circle theorem 3

A cyclic quadrilateral is a four-sided figure whose vertices lie in side and touch the circumference of the circle.  The opposite angles of C Cyclic quadrilateral lie in the opposite segment of the circle

Theorem 3

Opposite angles of a cyclic quadrilateral are supplementary.

Given: A cyclic quadrilateral PQRS

Proof; P Ô R = 2y (< at Centre = twice ∝ on the circumf.)
∴ 2x + 2y = 360^o (<s at a point)

2(x +y) = 360^o

X + y = 180^o