# Math Infographic, Geometry Problem 1346: Equilateral Triangle, Point on the Incircle,
Altitude, Perpendicular, Sum of Squares, Distance

### Proposition

The figure shows
an
equilateral triangle ABC with
altitude h and a point D on the
incircle.
DE= d, DF = e, and DG = f are
perpendicular to AB, BC, and AC,
respectively. Prove that d^{2} + e^{2} + f^{2} = h^{2}/2.

See solution below