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locus of projection so that a triangle is right

Source: 1st Mexican Mathematical Olympiad 1987 OMM P3

July 27, 2018
geometryLocusprojections

Problem Statement

Consider two lines ℓ\ell and ℓ′\ell ' and a fixed point PP equidistant from these lines. What is the locus of projections MM of PP on ABAB, where AA is on ℓ\ell , BB on ℓ′\ell ' , and angle ∠APB\angle APB is right?
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