1967 IMO Problems/Problem 4

Let A0B0C0 and A1B1C1 be any two acute-angled triangles. Consider all triangles ABC that are similar to ¢A1B1C1 (so that vertices A1;B1;C1 correspond to vertices A;B;C; respectively) and circumscribed about triangle A0B0C0 (where A0 lies on BC;B0 on CA; and AC0 on AB). Of all such possible triangles, determine the one with maximum area, and construct it.