Hi, I'm stuck on this problem and would like some help.

The purpose of this exercise is to prove the Nine-Point Circle Theorem. Let triangleABC be

a Euclidean triangle and let points D, E, F, L, M, N, and H be as in Figure 8.46. Let γ

be the circumscribed circle for triangleDEF.

a) Prove that quadrilateralEDBF is a parallelogram. Prove that DB=DN. Use a symmetry

argument to show that N lies on γ. Prove, in a similar way, that L and M lie on γ.

I have attached on how the picture looks like.