5.2.2.17 Construction problems

Condition: Given an angle and a point \( M \) inside it. Construct a \( \triangle A B C \) similar to the given \( \Delta A_{0} B_{0} C_{0} \), so that \( A \) and \( B \) belong to one side of the angle, the point \( C \) belongs to the other, and the side \( [B C] \) passes through the point \( M \).