Mathematics 4024 · O Level · Circles, arcs and sectors
Circles, arcs and sectors — practice question
A semicircle is shown with radii $OP$ and $OQ$ drawn in. A circle with centre $C$ touches the radii at $A$ and $B$, and also meets the semicircle at $T$. The circle has radius $1.8\text{ cm}$. $\angle BCA = 120^\circ$.
(a)[2]
Calculate the arc length of minor arc $AB$.
(b)[3]
The shaded part is enclosed by the circle and the radii $OP$ and $OQ$. Calculate the perimeter of this shaded region.
(c(i))[2]
Show that the radius of the semicircle comes to $5.4\text{ cm}$.
(c(ii))[1]
Calculate the length of the line segment $BQ$.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Appropriate sector formula” …