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MMO 293 Moscow MO 1955 locus, equal segments on sides of ABCD

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August 17, 2019
Locusequal segmentsgeometry

Problem Statement

Consider a quadrilateral ABCDABCD and points K,L,M,NK, L, M, N on sides AB,BC,CDAB, BC, CD and ADAD, respectively, such that KB=BL=a,MD=DN=bKB = BL = a, MD = DN = b and KL∦MNKL \nparallel MN. Find the set of all the intersection points of KLKL with MNMN as aa and bb vary.
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