MathDB

The diagonals

AD, BE

and

CF

of a convex hexagon concur at a point

M

. Suppose the six triangles

ABM, BCM, CDM, DEM, EFM

and

FAM

are all acute-angled and the circumcentre of all these triangles lie on a circle. Prove that the quadrilaterals

ABDE, BCEF

and

CDFA

have equal areas.

Problem Statement