In triangle ABC, angle C is 90 degrees, AB = 24, point M is the middle of side AB. Find the length of the line segment CM.

1) Triangle ABC rectangular with right angle C.

2) Since the median CM divides the side AB = 24 in half, then:

AM = MB = 24/2 = 12.

3) If the median is drawn from a right angle and divides the hypotenuse in half, then the median divides the angle C in half.

4) Consider m triangle AMC with right angle M.

Angle A = angle C = 45 °.

tg C = AM / CM;

tg 45 ° = 12 / CM;

1 = 12 / CM;

CM = 12;

Answer: CM = 12.