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2001 BAMO p2 collinear related to perpendiculars

Source:

August 26, 2019
collineargeometryperpendicular

Problem Statement

Let JHIZJHIZ be a rectangle, and let AA and CC be points on sides ZIZI and ZJ,ZJ, respectively. The perpendicular from AA to CHCH intersects line HIHI in XX and the perpendicular from CC to AHAH intersects line HJHJ in Y.Y. Prove that X,X, Y,Y, and ZZ are collinear (lie on the same line).
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