(a)[3]
Write the perimeter of the shaded region $PQT$ as a formula in $r$ and $\alpha$.
(b)[3]
When $\alpha = \frac{\pi}{3}$ and $r = 10$, determine the area of the shaded region correct to 2 significant figures.
Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The figure depicts a circle of radius $r$ cm with centre $O$. $PT$ is tangent to the circle at $P$, and $POT = \alpha$ radians. The line $OT$ intersects the circle at $Q$.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Valid expressions: $PT=r\tan\alpha$ and $QT=\frac{r}{\cos\alpha}-r$” …
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