Solve problems involving angles and tangents of circles

Angles and Tangents of Circles

6.4

Angles and Tangents of Circles

	Example

	The diagram below shows a circle centered at \(O\). Tangents \(PQ\) and \(RQ\) meet at a point \(Q\).

	Calculate the value of \(x\) and \(y\).

	Noted that \(\angle OPQ=90{^\circ}\) as \(OPQ\) is a right-angled triangle. So, \(\begin{aligned} x + 66{^\circ}&=90{^\circ} \\\\x&=90{^\circ} - 66{^\circ} \\\\x&=24{^\circ}.\\\\ \end{aligned} \) Also, the length of \(PQ\) is equal to the length of \(QR\). Thus, \(y=14\text{ cm}\).

Angles and Tangents of Circles

6.4

Angles and Tangents of Circles

	Example

	The diagram below shows a circle centered at \(O\). Tangents \(PQ\) and \(RQ\) meet at a point \(Q\).

	Calculate the value of \(x\) and \(y\).

	Noted that \(\angle OPQ=90{^\circ}\) as \(OPQ\) is a right-angled triangle. So, \(\begin{aligned} x + 66{^\circ}&=90{^\circ} \\\\x&=90{^\circ} - 66{^\circ} \\\\x&=24{^\circ}.\\\\ \end{aligned} \) Also, the length of \(PQ\) is equal to the length of \(QR\). Thus, \(y=14\text{ cm}\).