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.

See complete Problem 222 at:

gogeometry.com/problem/p222_viviani_theorem_equilateral_triangle_exterior.htm

Level: High School, SAT Prep, College geometry

## Monday, January 12, 2009

### Elearn Geometry Problem 222: Viviani Theorem, Exterior point

Labels:
distance,
equilateral,
exterior point,
perpendicular,
triangle,
Viviani theorem

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Join D to A & C. Now Tr. ABC = Area DABC - Tr ADC = Tr.DAB + Tr. DAC -Tr.ADC Hence,

ReplyDeleteTr.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

QED

Ajit: ajitathle@gmail.com