T makes TN perpendicular to AB and crosses AB to n.

If AT divides ∠BCA equally, there will be ∠CAT=∠NAT? ,

At rt δ cat？ And then what? RtδNAT includes ∠CAT=∠NAT, ∠ACT=∠ANT=90 degrees, and AT=AT.

So, rt δ cat? All equal? rtδNAT

So ∠NTA=∠CTA, CT = TN-①.

What is the delta delta sum? And then what? In δδATN, ∠DAM=∠TAN.

So, δ δ and? Similar to δδATN

So ∠ADM=∠ATN

And because ∠ADM=∠CDT (opposite to each other)

So ∠CDT=∠CTD, ∠CTD is an isosceles triangle CD = CT-②.

Simultaneous ① ②, CD = TM-③.

Because DE//AB, δδCDE is similar to δ TNB-④.

It is concluded from ③ and ④ that Δ Δ CDE is equal to Δ Δ TNB, then CE=TB.

That is CT+TE=TE+BE.

Therefore, CT=BE.

There are many letters and symbols in the process, not only in Chinese, so it takes a long time to input, but nevertheless, I am willing to help you input the process to solve this problem. I hope what I input can help you!