## 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, $$y=14\text{ cm}$$.