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Give a construction in which AC · BC is minimum

Source: Tournament of Towns 2007 - Fall - Senior O-Level - P3

September 4, 2011
geometrygeometry proposed

Problem Statement

Give a construction by straight-edge and compass of a point CC on a line ℓ\ell parallel to a segment ABAB, such that the product AC⋅BCAC \cdot BC is minimum.
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