MathDB

2005.1

Part of Swiss NMO - geometry

Problems(1)

equilateral criterion with medians and 2 cyclic quadrilaterals

Source: Switzerland - Swiss MO 2005 p1

7/19/2020
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.
geometryEquilateralMediansCentroidConcycliccyclic quadrilateral