Quick Notes

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, \(y=14\text{ cm}\).