Cho ΔABC vuông tại A có AH là đường cao

The problem involves a right triangle \( \Delta ABC \) with right angle at \( A \), and \( AH \) is the altitude from \( A \) to \( BC \). Let's break down the tasks provided:

a) You need to find the length of \( AH \) based on the given information.

b) You want to denote \( M \) and \( N \) as the feet of the perpendicular from \( A \) to \( AB \) and \( AC \), respectively, and then prove that \( AM \cdot AB = AN \cdot AC \).

c) You are asked to show that \( AH^2 = BC \cdot ANM \).

d) You need to prove that \( BC^2 = AH^2 + BM^2 + CN^2 \).

Each step requires applying properties of right triangles and the relationships between their sides and altitudes. If you have specific questions or further tasks, feel free to ask!