Question

$\frac{CP}{PA}=\frac{m}{3}$.Find $m$

Answer 1

In $△CAB$ and $△CPQ$,
$\angle ACB=\angle PCQ$ (Common angle)
$\angle CAB=\angle CPQ$ (Corresponding angles)
$\angle CBA=\angle CQP$ (Corresponding angles)
Thus, $△CAB\sim △CPQ$ (AAA rule)
$\frac{CP}{CA}=\frac{CQ}{CB}$
$\frac{CP}{CA}=\frac{4.8}{4.8+3.6}$
$\frac{CP}{CP+AP}=\frac{4.8}{8.4}$
$84CP=48CP+48AP$
$36CP=48AP$
$\frac{CP}{AP}=\frac{4}{3}$