Infographic Geometry Problem 1072: Triangle, Altitudes, Interior Point, Distance, Ratio. Level: High School, SAT Prep, College, Mathematics Education

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The figure shows a triangle ABC with an interior point P and the altitudes h_a, h_b, and h_c. If p_a, p_b, and p_c are the distances from P to the sides, prove that p_a / h_a + p_b / h_b + p_c / h_c = 1. See also: Artwork Problem 1072.

$Infographic Geometry problem: Triangle, Altitudes, Interior Point, Distance, Ratio$