
and

are acute-angled triangles. Describe, and prove, how to construct the triangle

with the largest possible area which is circumscribed about

(so

contains

contains

, and

contains

) and similar to
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$A_0B_0C_0$ and $A_1B_1C_1$ are acute-angled triangles. Describe, and prove, how to construct the triangle $ABC$ with the largest possible area which is circumscribed about $A_0B_0C_0$ (so $BC$ contains $B_0, CA$ contains $B_0$, and $AB$ contains $C_0$) and similar to $A_1B_1C_1.$