Prove that the height of an isosceles right-angled triangle, produced from the vertex of a right angle, is half the hypotenuse.

Around a right-angled triangle ABC, you can describe a circle whose radius is equal to half the length of its hypotenuse.
Then AC = D, AH = CH = BH = R, and therefore BH = R = D / 2 = AC / 2, as required.



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