SHARYGIN 2012 Problem 21
Two perpendicular lines pass through the orthocenter of an acute-angled triangle. The sidelines of the triangle cut on each of these lines two segments: one lying inside the triangle and another one lying outside it. Prove that the product of two internal segments is equal to the product of two external segments.
Nikolai Beluhov and Emil Kolev
Dataset text AI-MO AoPS. Quoted with source.
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