Let P be a point inside triangle ABC. Let AP meet BC at A1, let BP meet CA at B1, and let CP meet AB at C1. Let A2 be the point such that A1 is the midpoint of PA2, let B2 be the point such that B1 is the midpoint of PB2, and let C2 be the point such that C1 is the midpoint of PC2. Prove that points A2,B2, and C2 cannot all lie strictly inside the circumcircle of triangle ABC.(Australia) geometryIMO ShortlistIMO Shortlist 2019Triangle