# Prove that $MP \perp NP$

$$M$$ is the centre of the circumcentre of the cyclic quadrilateral $$ABCD$$. Let $$AB \cap DC = {N}$$ and $$(N, B, C) \cap (N, A, D) = P$$ ($$P \not\equiv N$$). Prove that $$MP \perp NP$$.

Notation: $$(X, Y, Z)$$ denotes the circumcircle of $$\triangle XYZ$$.

If you are wondering, this is adapted from a recent competition.

I have noticed that $$AMCP$$ and $$BMDP$$ is cyclic quadrilaterals. But I don't know if that is going to help with this problem.