This problem is in Vietnamese, and it concerns a triangle with specific geometric properties. Let's break down each part:

Part 1:

In the right triangle ABC, where $AB = BC$, the bisector of angle $\angle BAM$ intersects $BC$ at point D. The perpendicular line through D, which also goes through point C and intersects $BC$ at point N, is also given. The goal is to prove several things:

a) Prove that $AB = AE$.

This part requires proving the equality of segments AB and AE. Given the symmetric properties of the triangle and geometric construction, there are geometric principles, such as the angle bisector theorem and the properties of right triangles, that might help in proving this equality.

b) Calculate the value of $DAN$.

We need to compute the area or another property related to the geometric configuration mentioned.

c) Let $AB = a$. Prove that the perimeter of the triangle $DCB$ is $2a$.

This part asks to prove that the perimeter of a specific triangle is twice the length of one of its sides.

Part 2:

In this part, it deals with a right triangle $ABC$ with a given area of 1. Point $M$ is arbitrary in the plane, and you are asked to prove the inequality:

$MA \cdot BC + MB \cdot AC + MC \cdot AB \geq 4$

This is a geometric inequality, possibly related to geometric mean or an application of certain triangle inequalities.

Would you like a detailed solution for each part? Or do you want me to focus on a specific question? Let me know how you'd like to proceed!