Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
In the diagram, $A$ and $B$ lie on a circle of centre $O$ and radius $r$. The tangents at $A$ and $B$ intersect at $T$. The shaded region is enclosed by the minor arc $AB$ together with the lines $AT$ and $BT$. Angle $AOB$ measures $2\theta$ radians.
(i)[3]
Show that, in the situation where the area of sector $AOB$ is equal to the area of the shaded region, $\tan\theta = 2\theta$.
(ii)[3]
Given that $r = 8\text{ cm}$ and the minor arc $AB$ has length $19.2\text{ cm}$, find the area of the shaded region.
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme.