Trigonometry/Circles and Triangles/Viviani's theorem

Viviani's theorem is as follows:

Take any point P in an equilateral triangle. Drop perpendiculars from P to the three sides; let their feet be D, E, F. Then whatever the location of P, PD+PE+PF equals the altitude of the triangle.

If P is outside the triangle, this still holds provided that the perpendicular or perpendiculars lying entirely outside the triangle are treated as having negative length.

Last modified on 10 February 2011, at 18:45