MathDB

2

Part of 2023 Sharygin Geometry Olympiad

Problems(1)

perpendiculars from tangency spam inside rectangle

Source: Sharygin 2023 - P2 (Grade-8)

3/4/2023
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.
geometryrectangleperpendicular linesSharygin Geometry OlympiadSharygin 2023