Problem

Source: INAMO 2023 P1 (OSN 2023)

Tags: geometry, Indonesia, Indonesia MO, Inamo



An acute triangle $ABC$ has $BC$ as its longest side. Points $D,E$ respectively lie on $AC,AB$ such that $BA = BD$ and $CA = CE$. The point $A'$ is the reflection of $A$ against line $BC$. Prove that the circumcircles of $ABC$ and $A'DE$ have the same radii.