Cyclic Quadrilaterals

6.2  Cyclic Quadrilaterals

A cyclic quadrilateral is a quadrilateral in a circle where all four vertices of quadrilateral lie on the circumference of the circle.

  • The sum of opposite interior angles in a cyclic quadrilateral is \(180^\circ\).

The diagram below shows a cyclic quadrilateral \(PQRS\) and a straight line \(RST\).


Calculate the value of \(\angle PSR\).


First, calculate the value of \(y\).

\(\begin{aligned} \angle PQR + \angle PSR &= 180{^\circ} \\\\ 4y+ 2y&= 180{^\circ} \\\\6y&=180{^\circ} \\\\y&=30{^\circ}. \\\\\end{aligned}\)


\(\begin{aligned}\angle PSR&=30^\circ\times2 \\\\&=60^\circ. \end{aligned}\)