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We are given: and
Let , then
is inscribed in a semicircle.
. . Hence, is a right triangle.
is the altitude to the hypotenuse of a right triangle.
Theorem: The altitude to the hypotenuse of a right triangle is
. . the mean proportional of the two segments of the hypotenuse.
We have the quadratic: .
. . which factors: .
. . and has the positive root: .
Therefore: . cm.