Nemotron-IMO-Bench 2026 G1

The diagonals of the convex hexagon $A_1A_2\ldots A_6$ intersect at some point $M$ such that the circumcenters of the triangles $MA_iA_{i+1}$ ($1\leq i\leq 6$, with $A_7=A_1$) lie on a circle. Prove that the quadrilaterals $A_1A_2A_4A_5$, $A_2A_3A_5A_6$ and $A_3A_4A_6A_1$ have equal areas.