Question 4
The triangles $A_0B_0C_0$ and $A'B'C'$ have all their angles acute. Describe how to construct one of the triangles $ABC$, similar to $A'B'C'$ and circumscribing $A_0B_0C_0$ (so that $A,B,C$ correspond to $A',B',C'$, and $AB$ passes through $C_0$, $BC$ through $A_0$, and $CA$ through $B_0$). Among these triangles $ABC$ describe, and prove, how to construct the triangle with the maximum area.