Let ABC be a triangle with circumcircle ω. The bisector of ∠BAC intersects ω at point A1. Let A2 be a point on the segment AA1, CA2 cuts AB and ω at points C1 and C2, respectively. Similarly, BA2 cuts AC and ω at points B1 and B2, respectively. Let M be the intersection point of B1C2 and B2C1. Prove that MA2 passes the midpoint of BC.proposed by Jhefferson Lopez, Perú bisects segmentgeometrycircumcircle