BALKAN-SL 2020 G3

Let $ABC$ be a triangle. On the sides $BC$ , $CA$ , $AB$ of the triangle, construct outwardly three squares with centres $O_a$ , $O_b$ , $O_c$ respectively. Let $\omega$ be the circumcircle of $\vartriangle O_aO_bO_c$ . Given that $A$ lies on $\omega$ , prove that the centre of $\omega$ lies on the perimeter of $\vartriangle ABC$ .

Sam Bealing, United Kingdom