Let ABC be a triangle with circumcircle Γ and circumcentre O. Denote by M the midpoint of BC. The point D is the reflection of A over BC, and the point E is the intersection of Γ and the ray MD. Let S be the circumcentre of the triangle ADE. Prove that the points A, E, M, O, and S lie on the same circle.
geometrygeometry proposedcircumcircleCircumcentergeometry solvedHarmonic Quadrilateralsymmedian