Let ABC be an acut-angles triangle of incenter I, circumcenter O and inradius r. Let ω be the inscribed circle of the triangle ABC. A1 is the point of ω such that AIA1O is a convex trapezoid of bases AO and IA1. Let ω1 be the circle of radius r which goes through A1, tangent to the line AB and is different from ω . Let ω2 be the circle of radius r which goes through A1, is tangent to the line AC and is different from ω . Circumferences ω1 and ω2 they are cut at points A1 and A2. Similarly are defined points B2 and C2. Prove that the lines AA2,BB2 and CC2 they are concurrent. geometrycirclesinradiusconcurrencyconcurrent