The reasons are as follows

EF = AC

∴ Arc AFC= Arc ECF (same circle, equal chord, equal arc) ①

Arc AF= Arc ADC- Arc FC, Arc EC= Arc ECF- Arc FC ②.

Arc AF= Arc EC from ① ②

∠AEF degree = 1/2 arc AF degree (circle angle is equal to half of the corresponding radian number) ③

∠EAC degree = 1/2 arc EC degree (circle angle is equal to half of the corresponding radian number) ④

∠AEF=∠EAC ⑤ from ③ ④。

While the bisecting angle BAC of AD intersects BC. On D, a point on the intersecting circle O is E.

Therefore ∠BAE=∠EAC ⑥.

∠AEF =∠ BAE from ⑤ ⑤.

∴EF//AB (offset angles are equal and two straight lines are parallel).