In the triangle ABC, BM is the median and BH is the height. It is known that AC = 56 and BC = BM. Find HA.

Consider the triangle MBC. If BC = BM is an isosceles triangle, and the height of BH in an isosceles triangle is the median, then MH = HC.
From the condition BM – median, then AM = MC.
MC = MH + HC.
Start up HC – x.
Let’s compose and solve the equation.
AC = AM + MH + HC = 2x + x + x;
56 = 4x;
x = 56: 4;
x = 14.
We define AH.
AH = AM + MH = 2x + x = 3x = 3 * 14 = 48.
Answer: AH = 48.