∵ In the Rt triangle ABC, ∠ ACB = 90, BC = 3 and AC = 4.

∴AB=5

Perpendicular bisector on the side of AB intersects AB at point D0.

∴∠BDE=90=∠ACB,BD=BD=2.5

∠∠B =∠B here we go again.

∴∠A=∠E

Triangle ABC is similar to triangle EBD.

∴BD/BC=BE/BA

That is 2.5/3=BE/5.

∴BE=25/6

∫CE = BE-BC

∴CE=25/6-3=7/6