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loci of 5 points wanted if GH//BC or BCHG is inscriptible

Source: 1996 Romania NMO IX p4

August 13, 2024
geometryLocus

Problem Statement

In the triangle ABCABC the incircle JJ touches the sides BCBC, CACA, ABAB in DD, EE, FF, respectively. The segments (BE)(BE) and (CF)(CF) intersect JJ in G,HG,H. If BB and CC are fixed points, find the loci of points A,D,E,F,G,HA, D, E, F, G, H if GH∥BCGH \parallel BC and the loci of the same points if BCHGBCHG is an inscriptible quadrilateral.
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