Distances from the Centroid


	Let G be the centroid of the triangle ABC. Let A', B', and C' be the points on the circumcircle opposite to A, B, and C with respect to G. Then: . You can drag A, B, or C to change the figure.


	Contributed by: Jay Warendorff

Based on problem 723(b) in Crux Mathematicorum.

Circumcircle (Wolfram MathWorld)

Triangle Centroid (Wolfram MathWorld)

"Distances from the Centroid" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/DistancesFromTheCentroid/

Contributed by: Jay Warendorff

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Plane Geometry
Triangles

Browse all topics

The Sum of the Distances from the Orthocenter to the Vertices
Perpendiculars from the Midpoints of the Orthic Triangle
The Distance to the Orthocenter
Triangle Centroid
Parabolic Envelope from Congruent Triangles
Perpendicular Lines Generated by a Quadrilateral
A Geometrical Theorem of Leibniz
The Intersections of Extended Cevians with Three Circumcircles of Subtriangles
The Second Lemoine Circle
Area of a Triangle inside the Incircle

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