KöMaL 2025 B5465

Let $AA'$, $BB'$, and $CC'$ be diameters in the circumcircle of the non-equilateral acute triangle $ABC$. Let $A_1$ be the reflection of point $A'$ across line $BC$, $B_1$ be the reflection of $B'$ across line $AC$, and $C_1$ be the reflection of $C'$ across line $AB$. Prove that triangle $A_1B_1C_1$ is similar to triangle $ABC$.