Viviani's Theorem

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Let ABC be an equilateral triangle and let P be a point inside ABC. Draw perpendiculars PA', PB', and PC' from P to the sides of ABC. Because ABC is equilateral, the altitudes all have the same length; call that . Then PA' + PB' + PC' = .

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Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA


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