Mathematics 9709 · AS & A Level · Circular measure
Circular measure — practice question
The diagram represents a sector of a circle whose centre is $O$ and whose radius is $20\,\text{cm}$. Inside the sector is a circle with centre $C$ and radius $x\,\text{cm}$, touching the sector at $P$, $Q$ and $R$. Angle $POR = 1.2\,\text{radians}$.
(i)[4]
Show that $x = 7.218$, correct to $3$ decimal places, is obtained.
(ii)[2]
Find the total area of the three regions of the sector that are outside the circle with centre $C$.
(iii)[4]
Find the perimeter of the region $OPSR$ that is enclosed by the arc $PSR$ and the line segments $OP$ and $OR$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies $OQ=x+OC=20$” …