Let ABC be an isosceles triangle with base AC. Points D and E are chosen on the sides AC and BC, respectively, such that CD=DE. Let H,J, and K be the midpoints of DE,AE, and BD, respectively. The circumcircle of triangle DHK intersects AD at point F, whereas the circumcircle of triangle HEJ intersects BE at G. The line through K parallel to AC intersects AB at I. Let IH∩GF= {M}. Prove that J,M, and K are collinear points.
nicegeometrycollinearityjmmo2020circumcircleparallelogram