MathDB
3 tangential quadrilaterals given, equilateral triangle wanted

Source: Czech and Slovak MO, III A, 2003 p2

January 12, 2020
geometrytangential quadrilateralEquilateral

Problem Statement

On sides BC,CA,ABBC,CA,AB of a triangle ABCABC points D,E,FD,E,F respectively are chosen so that AD,BE,CFAD,BE,CF have a common point, say GG. Suppose that one can inscribe circles in the quadrilaterals AFGE,BDGF,CEGDAFGE,BDGF,CEGD so that each two of them have a common point. Prove that triangle ABCABC is equilateral.
Back to ProblemsView on AoPS