MathNet 2026 — Part 09 Question 30

Let $ABC$ be a triangle, and let the bisector of $\angle BAC$ meet $BC$ at $D$. Let $O, O_{1}, O_{2}$ be the circumcenters of triangles $ABC$, $ABD$, and $ADC$, respectively. Prove that $OO_{1} = OO_{2}$.