Given a non-isosceles triangle ABC, let D,E, and F denote the midpoints of the sides BC,CA, and AB respectively. The circle BCF and the line BE meet again at P, and the circle ABE and the line AD meet again at Q. Finally, the lines DP and FQ meet at R. Prove that the centroid G of the triangle ABC lies on the circle PQR.(United Kingdom) David Monk geometrycircumcircletrigonometrycomplex numbersgeometry proposed