Question

In need of some serious Geometry help:

Given triangle ABC, angle BAC=60 deg. Let BM and CN be angle bisectors and K be the incenter of ABC. Prove that quadrilateral ANKM can be inscribed.

Answer 1

So far, I drew what I think is the picture, but I just don't know where to start/

Answer 2

I know that if we show angle NKM= 120, that would suffice

Answer 3

because then opposite angles would be supplementary, but that would require showing that AKN and AKM are 30, 60, 90 rt triangles