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Centroid lies on the the circumcircle of the triangle PQR

Source: Romanian Master Of Mathematics 2012

March 3, 2012
geometrycircumcircletrigonometrycomplex numbersgeometry proposed

Problem Statement

Given a non-isosceles triangle ABCABC, let D,ED,E, and FF denote the midpoints of the sides BC,CABC,CA, and ABAB respectively. The circle BCFBCF and the line BEBE meet again at PP, and the circle ABEABE and the line ADAD meet again at QQ. Finally, the lines DPDP and FQFQ meet at RR. Prove that the centroid GG of the triangle ABCABC lies on the circle PQRPQR.
(United Kingdom) David Monk
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