Let ABC be a scalene triangle with circumcircle ω. The tangent to ω at A meets BC at D. The A-median of triangle ABC intersects BC and ω at M and N, respectively. Suppose that K is a point such that ADMK is a parallelogram. Prove that KA=KN. Proposed by Alexandru Lopotenco (Moldova) geometrygeometry proposedgeometry solvedparallelogramhumpty pointhumpty pointslengths