WAEC 2019 · Paper 2 · Q13

(a)
In the diagram, $\overline{RS}$ and $\overline{RT}$ are tangents to the circle with centre $O$ . $\angle TUS = 68^\circ$ , $\angle SRT = x$ and $\angle UTO = y$ . Find the value of $x$ .
(b)
Two tanks $A$ and $B$ are filled to capacity with diesel. Tank $A$ holds 600 litres of diesel more than tank $B$ . If 100 litres of diesel were pumped out of each tank, tank $A$ would then contain 3 times as much as tank $B$ . Find the capacity of each tank.
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Join $O$ to $S$ and $T$ .
$\angle SOT = 2\angle SUT$
$= 2 \times 68^\circ$
$= 136^\circ$ (angle at the centre is twice the angle at the circumference).
A tangent meets the radius at $90^\circ$ , so $\angle OSR = \angle OTR = 90^\circ$ .
The angles of quadrilateral $OSRT$ add up to $360^\circ$ : $x = 360^\circ - 90^\circ - 90^\circ - 136^\circ$
$= 44^\circ$ .

Let tank $B$ hold $b$ litres.
Tank $A$ holds 600 litres more, $b + 600$ .
After 100 litres are pumped out of each, they hold $b + 500$ and $b - 100$ , and $A$ then holds three times as much as $B$ : $b + 500 = 3(b - 100)$ .
Expand: $b + 500 = 3b - 300$ .
So $2b = 800$ and $b = 400$ .
Tank $A$ holds 1000 litres and tank $B$ holds 400 litres.