Answer to Question #228 in Geometry for salid

Question

M is the middle of the side AB of the triangle ABC. Prove that CM = AB/2 only if the angle ∠ACB = 90°.

Answer 1

Since AB/2 = AM = BM, CM = AB/2 only if the point C lies on a circle with a diameter AB. And that's why ∠ACB = 90°.