JAMB 1993 · UME · Q32

In the diagram, $\angle QPS = \angle SPR$ , $PR = 9$ cm, $PQ = 4$ cm and $QS = 3$ cm. Find $SR$ .

Worked solution (try it first)

$PS$ bisects $\angle QPR$ .
The angle bisector divides the opposite side in the ratio of the other two sides: $\dfrac{QS}{SR} = \dfrac{PQ}{PR}$ .
So $\dfrac{3}{SR} = \dfrac{4}{9}$ , which gives $4 \times SR = 27$ .
$SR = \frac{27}{4} = 6\frac34$ cm, option A.