Monday, January 12, 2009

Elearn Geometry Problem 222: Viviani Theorem, Exterior point

Equilateral Triangle, Exterior Point
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.

 Geometry Problem 222. Viviani Theorem
See complete Problem 222 at:

Level: High School, SAT Prep, College geometry

1 comment:

  1. Join D to A & C. Now Tr. ABC = Area DABC - Tr ADC = Tr.DAB + Tr. DAC -Tr.ADC Hence,
    Tr.ABC = Tr.DAB + Tr. DAC -Tr.ADC or
    AC*h/2 = AB*f/2 + AC*e/2 - AC*g/2 or
    h = f + e - g