Cool theorem - angle bisector

In #math

I was helping my daughter with geometry the other day and this cute theorem popped up in the examples. For some reason I don't recall ever seeing it before, and it struck me as somehow particularly elegant. I have used (many times) the specific - more limited version with isosceles triangles - but to see the generalization was just neat.

It makes me wonder also why I find enjoyment in something this simple and technical.