Build a Square on a Given SideGeometric Construction with the Compass AloneBuild a square with a given side AB. SolutionUsing Problem #4 first construct CA perpendicular to AB. Draw the circle A(B) of radius AB and center A and another centered at C and intersecting the former in points, say, M and N. We are given then circle A(B) and an arc MN that can be bisected following the construction in Problem #7. Both thus found points will lie on AC at the distance from A equal to AB. Denote one of them D: Swing two arcs of radius AB - one centered at D, another at B. The arcs will intersect at A and another point, say, E. The quadrilateral ADEB is a square. Problems (Use a compass only)
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