Mathematics 9709 · AS & A Level · Circular measure

Circular measure — practice question

The figure shows $OAXB$ as a sector of a circle centred at $O$ with radius $10\,\text{cm}$. The chord $AB$ has length $12\,\text{cm}$. Line $OX$ passes through $M$, the midpoint of $AB$, and $OX$ is perpendicular to $AB$. The shaded part is enclosed by the chord $AB$ and the arc of a circle centred at $X$ with radius $XA$.
(i)[3]

Show that angle $AXB$ is $2.498$ radians, correct to $3$ decimal places.

(ii)[3]

Find the total perimeter of the shaded region.

(iii)[3]

Find the total area of the shaded region.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Use the midpoint and Pythagoras’ theorem to determine the lengths

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