It is known that in the right triangle ABC, AB=AC, BD bisects the angle ABC, the extension line of CE perpendicular to BD intersects at E, and the extension lines of BA and Ce intersect at F. ..

Prove:

∵BE⊥CF

∴∠BEF=∠BEC=90

∵∠ABE=∠CBE,AE=AE。

∴△ABE≌CBE

∴AF=AC=

△ BCF is an isosceles triangle.