Go Geometry Problem Problem 222. Viviani's Theorem, Equilateral Triangle, Point, Altitude, Distance

For a given point D outside an equilateral triangle ABC, the sum of the distances DE and DF minus DG from the point D to the sides BC, AB and AC respectively is equal to the altitude of the triangle.
 

Viviani theorem exterior point
 


The theorem is named for Vincenzo Viviani (1622-1703), 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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