It looks like you've uploaded a geometry problem in Vietnamese related to a square with several conditions and properties to prove. Let me break down the tasks from the problem for you and proceed with the first question.

Here are the parts of the problem you want to prove:

• a) Prove that $EF \parallel BM$.
• b) Prove that triangle $\Delta OEF$ is right-angled.
• c) Show that the three points $O, F, H$ are collinear.
• d) Given that point $P$ is on segment $DC$ such that $\angle FAP = 45^\circ$, prove that the distance from point $A$ to point $FP$ remains constant as point $F$ moves.

I will start by analyzing part a) where we need to prove that $EF \parallel BM$. To proceed, I will need to understand the geometric relationships in the diagram.

Would you like me to focus on one part of the question at a time, or would you like an overall breakdown of the problem first? Feel free to let me know!