JAMB 2015 · UTME · Q39✱

In $\triangle MNO$ , $MN = 9$ units, $MO = 6$ units and $NO = 12$ units. If the bisector of angle $M$ meets $NO$ at $P$ , calculate $NP$ .

Worked solution (try it first)

The bisector of $\angle M$ cuts $NO$ in the ratio of the sides next to $M$ : $NP : PO = MN : MO = 9 : 6$ , which is $3 : 2$ .
$NO = 12$ is split into $3 + 2 = 5$ parts, so $NP = \frac35 \times 12$ .
So $NP = 7.2$ units, option B.