MathDB
equilateral criterion with medians and 2 cyclic quadrilaterals

Source: Switzerland - Swiss MO 2005 p1

July 19, 2020
geometryEquilateralMediansCentroidConcycliccyclic quadrilateral

Problem Statement

Let ABCABC be any triangle and D,E,FD, E, F the midpoints of BC,CA,ABBC, CA, AB. The medians AD,BEAD, BE and CFCF intersect at point SS. At least two of the quadrilaterals AFSE,BDSF,CESDAF SE, BDSF, CESD are cyclic. Show that the triangle ABCABC is equilateral.
Back to ProblemsView on AoPS