Let ABC be an equilateral triangle with K its circumcircle.

Let P be a point on K (different from A, B, and C) and m 
the tangent line to K at point P.

Let D, E, and F be points on m such that AD, BE, and CF 
are perpendicular to m.

Prove that |AD| + |BE| + |CF| equals twice the length of 
an altitude of triangle ABC.