The Area of the Pedal Triangle of the Centroid

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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
be
and the area of ABC be
. Then
.
Contributed by: Jay Warendorff (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
See Problem 5 in N. Altshiller-Court, College Geometry, 2nd ed., Mineola, NY: Dover, 2007 p. 71.
Permanent Citation
"The Area of the Pedal Triangle of the Centroid"
http://demonstrations.wolfram.com/TheAreaOfThePedalTriangleOfTheCentroid/
Wolfram Demonstrations Project
Published: March 7 2011