Problems(1)
Let ABC be a triangle with a right angle at C. Let I be the incentre of triangle ABC, and let D be the foot of the altitude from C to AB. The incircle ω of triangle ABC is tangent to sides BC, CA, and AB at A1, B1, and C1, respectively. Let E and F be the reflections of C in lines C1A1 and C1B1, respectively. Let K and L be the reflections of D in lines C1A1 and C1B1, respectively. Prove that the circumcircles of triangles A1EI, B1FI, and C1KL have a common point. geometryRMMRMM 2020