The inscribed circle ω of triangle ABC with center I touches the sides AB,BC,CA at points C1,A1,B1. The circle circumsrcibed around △AB1C1 intersects the circumscribed circle of ABC for second time at the point K. Let M be the midpoint BC, L be the midpoint of B1C1. The circle circumsrcibed around △KA1M cuts intersects ω for second time at the point T. Prove that the circumscribed circles of triangles KLT and LIM are tangent. geometrytangent circlesUkrainian TYM