In triangle ABC, the median BM and the height AH are drawn. Find HM if AC = 16 cm.

1. AM = CM, since ВM, according to the problem statement, is the median and separates the side of the triangle, to which it is drawn on two equal segments.

2. Triangle AСН is rectangular, since AН is height according to the problem statement.

3. In the indicated triangle НM is the median, since it divides the AC into two identical segments. AС in this triangle is the hypotenuse.

4. The median drawn from a right angle to the hypotenuse is equal to its half.

That is, НM = AC: 2 = 16: 2 = 8 centimeters.

Answer: the length of НM is 8 centimeters.