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locus P such that 4 angle bisectors create a parallelogram

Source: TOT 477 1995 Autumn S A1 - Tournament of Towns

July 9, 2024
geometryangle bisectorLocusparallelogram

Problem Statement

If P is a point inside a convex quadrilateral ABCDABCD, let the angle bisectors of ∠APB\angle APB, ∠BPC\angle BPC, ∠CPD\angle CPD and ∠DPA\angle DPA meet ABAB, BCBC, CDCD and DADA at KK, LL, MM and NN respectively.
(a) Find a point PP such that KLMNKLMN is a parallelogram. (b) Find the locus of all such points PP.
(S Tokarev)
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