In the triangle ABC, the median BM and the height BH. It is known that AC = 17 and BC = BM. Find AH.

Given:
triangle ABC;
BM is the median;
BH – height;
AC = 17;
BC = BM;
Find the length of AH -?
Decision:
1) AM = MC as, according to the condition of the problem, BM is the median. Hence
AM = MC = 1/2 * AC;
AM = MC = 1/2 * 17;
AM = MS = 8.5;
2) Consider the triangle BMC. By the condition BC = BM, then the triangle of the BMC is isosceles. Then the HV height is also the median. Hence:
MH = HC = 1/2 * MS;
MH = HC = 1/2 * 8.5;
MH = HC = 4.25;
3) AH = AM + MH;
AH = 8.5 + 4.25;
AH = 12.75.
Answer: 12.75.