The hypotenuse of a right-angled triangle is 14. Find the median from a right angle.

We describe a circle around a right-angled triangle ABC with a center at point O.

The inscribed angle ACB = 90 and rests on the arc AB, then the degree measure of the arc AB = 180, and therefore the hypotenuse AB is the diameter of the circumscribed circle.

Then ОА = ОВ = R = AB / 2 = 14/2 = 7 cm.

The median OС is the radius of the circumscribed circle, then OС = OA = OB = 7 cm.

Answer: The median length is 7 cm.

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