IMO 2016 Shortlist G1
In a convex pentagon ABCDE, let F be a point on AC such that ∠FBC = 90◦ . Suppose triangles ABF, ACD and ADE are similar...
Category: Geometry
Problem
In a convex pentagon ABCDE, let F be a point on AC such that ∠FBC = 90◦ . Suppose triangles ABF, ACD and ADE are similar isosceles triangles with ∠FAB = ∠FBA = ∠DAC = ∠DCA = ∠EAD = ∠EDA. Let M be the midpoint of CF. Point X is chosen such that AMXE is a parallelogram. Show that BD,EM and FX are concurrent.