Problem:
A triangle, two of whose sides are and , is inscribed in a circle. Find the minimal possible radius of the circle.
Solution
Solution:
Since the circle has a chord of length , its diameter is at least and so its radius is at least . To achieve equality, choose a right triangle with hypotenuse and one leg (the other leg will, by the Pythagorean theorem, have length ). Then the midpoint of the hypotenuse is the center of a circle of radius passing through all three vertices.
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