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

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