okay this one is from Prof. Mircea Lascu from Zalau, Romaniaand Prof. V. Cartoaje from Ploiesti, Romania. It goes like this: given being a triangle ABC for every point M inside we construct the points AM, BM, CM on the circumcircle of the triangle ABC such that A, AM, M are collinear and so on. Find the locus of these points M for which the area of the triangle AM BM CM is bigger than the area of the triangle ABC.
geometrycircumcircleratioReally oldgeometry unsolvedalgebra