ABC is an acute triangle with AB>AC. ΓB is a circle that passes through A,B and is tangent to AC on A. Define similar for ΓC. Let D be the intersection ΓB and ΓC and M be the midpoint of BC. AM cuts ΓC at E. Let O be the center of the circumscibed circle of the triangle ABC. Prove that the circumscibed circle of the triangle ODE is tangent to ΓB. geometrycircumcircletangent circlescircles