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perpendiculars from tangency spam inside rectangle

Source: Sharygin 2023 - P2 (Grade-8)

March 4, 2023
geometryrectangleperpendicular linesSharygin Geometry OlympiadSharygin 2023

Problem Statement

The diagonals of a rectangle ABCDABCD meet at point EE. A circle centered at EE lies inside the rectangle. Let CFCF, DGDG, AHAH be the tangents to this circle from CC, DD, AA; let CFCF meet DGDG at point II, EIEI meet ADAD at point JJ, and AHAH meet CFCF at point LL. Prove that LJLJ is perpendicular to ADAD.
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