Let ABCD be an isosceles trapezoid with AB∥CD. Let E be the midpoint of AC. Denote by ω and Ω the circumcircles of the triangles ABE and CDE, respectively. Let P be the crossing point of the tangent to ω at A with the tangent to Ω at D. Prove that PE is tangent to Ω.Jakob Jurij Snoj, Slovenia RMMRMM 2019geometryComplex GeometryInversion