PL-OM 2021 Problem 5

A convex hexagon $ABCDEF$ is given where $\measuredangle FAB + \measuredangle BCD + \measuredangle DEF = 360^{\circ}$ and $\measuredangle AEB = \measuredangle ADB$ . Suppose the lines $AB$ and $DE$ are not parallel. Prove that the circumcenters of the triangles $\triangle AFE, \triangle BCD$ and the intersection of the lines $AB$ and $DE$ are collinear.