Problem 221. Viviani's Theorem, Equilateral Triangle,
Point, Altitude, Distance

In an equilateral triangle, prove that the sum of the distances from any interior point to the sides is equal to the altitude of the triangle.
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The theorem is named for Vincenzo Viviani (16221703), a pupil of Galileo and Torricelli, who is also remembered for a reconstruction of a book on the conic sections of Apollonius and for finding a way of trisecting an angle through the use an equilateral hyperbola.
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