MathNet 2023-part-03 — 191 problems (EN–VI) Question 144

Let $ABC$ be an acute triangle and $H$ a point in the interior of the triangle such that $AB^{2} + CH^{2} = BC^{2} + AH^{2} = AC^{2} + BH^{2}$. Prove that $H$ is the orthocenter of triangle $ABC$.