3.16: Composite sectors with a parallel chord

0606/12/M/J/25 — Question 10 · 8 marks

The diagram shows the shape $OABCDEF$.

$AOF$ is a straight line.

$OAB$ and $OEF$ are sectors of a circle with centre $O$ and radius $r$.

Angle $BOA =$ angle $EOF$.

$OCD$ is a sector of a circle with centre $O$ and radius $\dfrac{4r}{3}$.

Angle $COD$ is $\theta$ radians.

The point $B$ lies on the line $OC$ and the point $E$ lies on the line $OD$.

The line $BE$ is parallel to the line $AOF$.

(a)

Find, in terms of $r$ and $\theta$, the area of the shaded region $BCDE$.

[3]

▸ Answer

(b)

The diagram shows the shape from part (a) with region $OABEF$ shaded.

Find, in terms of $r$ and $\theta$, the perimeter of the shaded region.

[5]

▸ Answer