MathDB
Prove quadrilateral EFGH is a rectangle iff ABCD concyclic

Source: CWMO 2003, Problem 6

December 27, 2008
geometryrectangleparallelogramgeometry unsolved

Problem Statement

A circle can be inscribed in the convex quadrilateral ABCD ABCD. The incircle touches the sides AB,BC,CD,DA AB, BC, CD, DA at A1,B1,C1,D1 A_1, B_1, C_1, D_1 respectively. The points E,F,G,H E, F, G, H are the midpoints of A1B1,B1C1,C1D1,D1A1 A_1B_1, B_1C_1, C_1D_1, D_1A_1 respectively. Prove that the quadrilateral EFGH EFGH is a rectangle if and only if A,B,C,D A, B, C, D are concyclic.
Back to ProblemsView on AoPS