Yi Zheng ∠BCE=∠BDC.

And < BFC = < BDC+< FCD.

So ∠BCF=∠BFC=∠BDC+∠FCD=∠BCE+∠ECF

So BF=BC

(2) From Pythagorean Theorem, BD=√3*3+4*4=5.

CE= 12/5 is obtained by equal area method, and BE=9/5 is obtained by pythagorean theorem.

Use Pythagorean Theorem to get EF=3-9/5=6/5, and then CF = 6/5 √ 5 (6/5 times the root number 5).