Let ABC be an isosceles triangle with vertex A and AB>BC. Let k be the circle with center A passsing through B and C. Let H be the second intersection of k with the altitude of the triangle ABC through B. Further let G be the second intersection of k with the median through B in triangle ABC. Let X be the intersection of the lines AC and GH. Show that C is the midpoint of AX.
geometrymidpointisoscelesequal segments