# Answer to Question #228 in Geometry for salid

Question #228

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

Expert's answer

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°.

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