MathNet 1989 — Part 01 Question 32

$ABC$ is a triangle. $A'$, $B'$, $C'$ are points on the segments $BC$, $CA$, $AB$ respectively. $\angle B'A'C' = \angle A$ and $\dfrac{AC'}{C'B} = \dfrac{BA'}{A'C} = \dfrac{CB'}{B'A}$. Show that $ABC$ and $A'B'C'$ are similar.