In a right-angled triangle ABC with a right angle B, the median BM = 17 and the leg BA = 16 are known

In a right-angled triangle ABC with a right angle B, the median BM = 17 and the leg BA = 16 are known. Find the BC leg of this triangle.

Since the rectangle ABC is rectangular, and point M is the middle of the hypotenuse AC, a circle can be described around the triangle, the center of which will be point M.

Then the segments AM, BM, CM are the radii of this circle.

According to the condition BM = 17 cm, then the hypotenuse of the AC is the diameter of the circle and will be equal to:

AC = 2 * R = 2 * BM = 2 * 17 = 34 cm.

Then, by the Pythagorean theorem, BC ^ 2 = AC ^ 2 – AB ^ 2 = 34 ^ 2 – 16 ^ 2 = 1156 – 256 = 900.

BC = 30 cm.

Answer: The length of the BC leg is 30 cm.