Let ABC be a triangle with circumcircle c and circumcenter O, and let D be a point on the side BC different from the vertices and the midpoint of BC. Let K be the point where the circumcircle c1 of the triangle BOD intersects c for the second time and let Z be the point where c1 meets the line AB. Let M be the point where the circumcircle c2 of the triangle COD intersects c for the second time and let E be the point where c2 meets the line AC. Finally let N be the point where the circumcircle c3 of the triangle AEZ meets c again. Prove that the triangles ABC and NKM are congruent. geometrycongruent trianglescircumcircle