Question 54
Let $X$, $Y$, and $Z$ be the points on the sides $BC$, $CA$, and $AB$ of the triangle $ABC$, such that $\triangle XYZ \sim \triangle ABC$ ($\angle X = \angle A$, $\angle Y = \angle B$). Prove that the orthocenter of $\triangle XYZ$ coincides with the circumcenter of $\triangle ABC$.