MathDB
Similar triangles and cyclic quadrilaterals

Source: JBMO Shortlist 2002

November 12, 2008
geometry proposedgeometry

Problem Statement

Let ABC ABC be a triangle with centroid G G and A1,B1,C1 A_1,B_1,C_1 midpoints of the sides BC,CA,AB BC,CA,AB. A paralel through A1 A_1 to BB1 BB_1 intersects B1C1 B_1C_1 at F F. Prove that triangles ABC ABC and FA1A FA_1A are similar if and only if quadrilateral AB1GC1 AB_1GC_1 is cyclic.
Back to ProblemsView on AoPS