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locus of projection inside a square, fixed triangle perimeter

Source: Moldova JBMO TST 2002 2.3

July 10, 2020
geometryLocusperimeterangle

Problem Statement

The side of the square ABCDABCD has a length equal to 11. On the sides (BC)(BC) ¸and (CD)(CD) take respectively the arbitrary points MM and NN so that the perimeter of the triangle MCNMCN is equal to 22. a) Determine the measure of the angle ∠MAN\angle MAN. b) If the point PP is the foot of the perpendicular taken from point AA to the line MNMN, determine the locus of the points PP.
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