MathDB
Convex hexagon

Source: TST 2014 of Tajikistan

May 20, 2014
geometrycircumcircleLaTeXgeometry proposed

Problem Statement

In a convex hexagon ABCDEFABCDEF the diagonals AD,BE,CFAD,BE,CF intersect at a point MM. It is known that the triangles ABM,BCM,CDM,DEM,EFM,FAMABM,BCM,CDM,DEM,EFM,FAM are acute. It is also known that the quadrilaterals ABDE,BCEF,CDFAABDE,BCEF,CDFA have the same area. Prove that the circumcenters of triangles ABM,BCM,CDM,DEM,EFM,FAMABM,BCM,CDM,DEM,EFM,FAM are concyclic.
Proposed by Nairy Sedrakyan
Back to ProblemsView on AoPS