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Problem 620

Inscribe a square in a given semicircle.

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To inscribe a square in a given semicircle, first draw the semicircle and diameter AB with center O. Mark the midpoint C of diameter AB, construct two perpendicular bisectors to AB at points A and C, meeting at point P. Then, construct a perpendicular bisector to segment PB at point B, intersecting the semicircle at point Q. The vertices of the inscribed square are A, P, B, and Q, with side length s, where \(2s = d\) (d is the diameter of the semicircle).

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