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Altitudes and Incircles

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Let ABC be an acute triangle with altitudes AA', BB', and CC'. The sum of the altitudes is equal to the sum of the semiperimeter and the radii of the six incircles of the triangles XYZ formed by the altitudes and the sides:

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

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