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.