Question

D is a point on the side BC of a $\Delta ABC$ such that $\angle ADC=\angle BAC$. Show that $C{A}^2=CB.CD$.

Answer 1

$\Delta ADC$ and $\Delta BAC$ are similar (Using AA criterion)

$\Rightarrow \frac{CA}{CB}=\frac{CD}{CA}$

$C{A}^2=CB.CD$