Hi, after trying to figure out this problem for a few hours i think i need some guidance.

The question is given AB=BC=15, and AC=18, and ADEF is a rhombus.

How do i find 1.) the side of the rhombus and 2.) the radius of a inscribed circle of the rhombus?

Here is a picture the teacher gave us, not drawn to scale.

I know triangle ABC is isosceles , and triangle DBE and FEC are congruent and my intuition tells me the side length of the rhombus is 9, but i don't know how to prove it.