MathDB

4

Part of 2014 Tajikistan Team Selection Test

Problems(1)

Convex hexagon

Source: TST 2014 of Tajikistan

5/20/2014
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
geometrycircumcircleLaTeXgeometry proposed