Go Geometry Problem Problem 223. Viviani's Theorem, Isosceles Triangle, Altitude, Distance

In an isosceles triangle ABC (AB = BC), the sum of the distances from any point on AC to the equal sides is equal to the altitude of the equal sides. View or post a solution.
 

Viviani theorem, Isosceles triangle
 


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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