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Locus of incenter, variable point on BC

Source: 2022 Israel TST 3 P1

May 22, 2022
geometryincenter

Problem Statement

A triangle ABCABC with orthocenter HH is given. PP is a variable point on line BCBC. The perpendicular to BCBC through PP meets BHBH, CHCH at XX, YY respectively. The line through HH parallel to BCBC meets APAP at QQ. Lines QXQX and QYQY meet BCBC at UU, VV respectively. Find the shape of the locus of the incenters of the triangles QUVQUV.
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