MathNet 1999 — Part 01 Question 7

Given a triangle $ABC$, explain how to construct with ruler and compass a triangle $A'B'C'$ of minimum area such that $C' \in AC$, $A' \in AB$, $B' \in BC$ and $\angle B'A'C' = \angle BAC$, $\angle A'C'B' = \angle ACB$.