Six Incircles in an Equilateral Triangle
Six Incircles in an Equilateral Triangle
From an interior point P of an equilateral triangle ABC draw lines perpendicular to the sides. Let A', B', and C' be the points on the sides opposite A, B and C. Inscribe circles in the six subtriangles. Let (XYZ) denote the diameter of the incircle in triangle XYZ.
d
Then the sum of the diameters of the red circles equals the sum of the diameters of the blue circles:
d
d
d
d
d
d