Connecting BD

BCE is a right triangle with double vertical graphs, which is proved by projective theorem or similarity.

BC square =CD*CE

Substitute the formula on your left to get CD/CE, and the conclusion you want is =DE/CE.

Unless we prove that CD=DE is based on the angular bisector, we have CD=BE.

If CD=DE must be a BCE isosceles right triangle, then the angle BAC is 90 degrees.

So your conclusion is wrong. It should be, not Germany.