# Acute-angled triangle ABC. BM median, BH height. If MH = 10cm then find the length AC.

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

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

3. In the indicated triangle НM is the median, since it divides AC into two identical segments AM and CM.

4. AC in this triangle is the hypotenuse.

5. According to the theorem, the median drawn from a right angle to the hypotenuse is equal to its half.

That is, AC = MH x 2 = 10 x 2 = 20 centimeters.

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