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Connect the feet of the perpendiculars from the centroid of the triangle ABC to its sides to form the pedal triangle

of the centroid. Let the area of

and the area of ABC be

. Then

See Problem 5 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 71.

Contributed by: Jay Warendorff

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The Area of the Pedal Triangle of the Centroid