The points P and Q lie on a circle, with centre O and radius 8 cm, such that \({\rm{P\hat OQ}} = 59^\circ \) .

Find the area of the shaded segment of the circle contained between the arc PQ and the chord [PQ].

area of triangle \({\text{POQ}} = \frac{1}{2}{8^2}\sin 59^\circ \)     M1

= 27.43     (A1)

area of sector \( = \pi {8^2}\frac{{59}}{{360}}\)     M1

= 32.95     (A1)

area between arc and chord \( = 32.95 - 27.43\)

\( = 5.52{\text{ (c}}{{\text{m}}^2})\)     A1

[5 marks]

This was an easy starter question, with most candidates gaining full marks. Others lost marks through premature rounding or the incorrect use of radian measure.