Because ∠ b = 45.

So ∠ BAE = 45∠ AEB = 90.

Because AEF = 45.

So ∠ cef = 45.

Because isosceles right-angled trapezoid ABCD

So ∠ c = ∠ b = 45

So EFC = 90.

So CE= radical 2 CF

Because BE=3/2* root number 2 (not proved here) BC=4* root number 2.

So CE=5/2* root number 2

So CF=5/2

(2) when AB=BE

Connecting AE

Because AB=3 (not proved here)

So BE=3

Because ∠ b = 45.

So ∠ AEB = 67.5.

Because AEF = 45.

So ∠ BEF = 1 12.5.

So ∠ FEC = 67.5.

Because ∠ c = 45.

So ∠ EFC = 67.5.

So CE=CF

Because CE=BC-BE=4* radical number 2-3

So CF=4* radical number 2-3

(3) When AE=AB=3

Because ∠ b = 45.

So ∠ AEB = 45.

Because AEF = 45.

So ∠ FEC = 90.

Because ∠ c = 45.

So CF= root 2CE

Because AE = AB = 3 ∠ B = 45.

So BE=3* radical number 2

Because BC=4* radical number 2

So CE= root number 2

So CF=2