<Tri-2024-2117>, hint

Let M be the midpoint of AB, O be the circumcenter of  triangle ABC.

Construct the circumcircle w of triangle AOB, <AOB=120=2 x 60 (<BCA)

Let T be the interection  of CM with w.

Let P, Q be the intersections of  lines AT and BT with BC, AC respectively.

Then PQ //AB, by Ceva's theorem