WAEC 2021 · Paper 2 · Q11

(a)
In the diagram, $O$ is the centre of the circle $PRSTU$ and $\angle PTS = 58^\circ$ . Find: (i) $\angle POS$ ; (ii) $\angle PRS$ .
Separate values with commas, e.g. 3, −2
(b)
Ato, Bonsu and Musah have a joint business venture. They agreed to raise the capital as follows: Ato GH¢ 2,000.00 per month for 2 months; Bonsu GH¢ 3,000.00 for one month; and Musah GH¢ 2,500.00 per month for 3 months. It was also agreed that profit would be shared in proportion to the total amount contributed by each partner. If the profit at the end of a period was GH¢ 5,220.00, calculate Ato's profit as a percentage of his contribution.

Worked solution (try it first)

The angle at the centre is twice the angle at the circumference on the same arc: $\angle POS = 2 \times \angle PTS$
$= 116^\circ$ .

$PRST$ is a cyclic quadrilateral, so opposite angles add up to $180^\circ$ : $\angle PRS = 180^\circ - 58^\circ$
$= 122^\circ$ .

Total contributions: Ato $2 \times 2000 = 4000$ , Bonsu 3000, Musah $3 \times 2500 = 7500$ .
Ratio $4000 : 3000 : 7500 = 8 : 6 : 15$ (29 parts).
Ato's profit $= \frac{8}{29} \times 5220 =$ GH¢ 1,440.
As a percentage of his contribution: $\frac{1440}{4000} \times 100\% = 36\%$ .