Cyclic Quadrilaterals

Cyclic Quadrilaterals

6.2

Cyclic Quadrilaterals

	Definition

	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 \(180^\circ\).

	Example

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

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

	First, calculate the value of \(y\). \(\begin{aligned} \angle PQR + \angle PSR &= 180{^\circ} \\\\ 4y+ 2y&= 180{^\circ} \\\\6y&=180{^\circ} \\\\y&=30{^\circ}. \\\\\end{aligned}\) Thus, \(\begin{aligned}\angle PSR&=30^\circ\times2 \\\\&=60^\circ. \end{aligned}\)

Cyclic Quadrilaterals

6.2

Cyclic Quadrilaterals

	Definition

	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 \(180^\circ\).

	Example

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

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

	First, calculate the value of \(y\). \(\begin{aligned} \angle PQR + \angle PSR &= 180{^\circ} \\\\ 4y+ 2y&= 180{^\circ} \\\\6y&=180{^\circ} \\\\y&=30{^\circ}. \\\\\end{aligned}\) Thus, \(\begin{aligned}\angle PSR&=30^\circ\times2 \\\\&=60^\circ. \end{aligned}\)