1967 IMO Problems/Problem 4

Let $A_0B_0C_0$ and $A_1B_1C_1$ be any two acute-angled triangles. Consider all triangles $ABC$ that are similar to $\triangle A_1B_1C_1$ (so that vertices $A_1$ , $B_1$ , $C_1$ correspond to vertices $A$ , $B$ , $C$ , respectively) and circumscribed about triangle $A_0B_0C_0$ (where $A_0$ lies on $BC$ , $B_0$ on $CA$ , and $AC_0$ on $AB$ ). Of all such possible triangles, determine the one with maximum area, and construct it.

$\textbf{Solution:}$ The solution to this problem can be found here: [1]

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1967 IMO Problems/Problem 4