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collinear wanted, peprpendiculars around a rectangle

Source: OLCOMA Costa Rica National Olympiad, Final Round, 2016 Shortlist G3 day1

September 23, 2021
collineargeometryrectangle

Problem Statement

Let the JHIZJHIZ be a rectangle and let AA and CC be points on the sides ZIZI and ZJZJ, respectively. The perpendicular from AA on CHCH intersects line HIHI at point XX and perpendicular from CC on AHAH intersects line HJHJ at point YY. Show that points X,YX, Y, and ZZ are collinear.
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