In triangle ABC, AB = BC, two bisectors AK and CM are drawn. Prove that MK is parallel to AC.

Since the ABC triangle is isosceles, and the AK and CM are bisectors of equal angles, then the angle ОАС = OCA, and then the AOС triangle is isosceles.

The bisectors of an isosceles triangle drawn from the angles at the base are equal, then AK = CM, and since OA = OС, then OM = OK, and then the MOK triangle is isosceles.

The triangles MOC and AOС are similar in two proportional sides and the angle between them, and then the angle OMC = OCA, and since these are criss-cross angles, the MC is parallel to the AC, which was required to be proved.