Investigating circumcentres of iterated median triangles

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Investigation: Circumcentres of iterated median triangles
Start with any ΔABC and construct its circumcentre O as shown below. Label the midpoints of the sides BC, CA and AB respectively as A1, B1 and C1 as shown below. Repeat the process with the new ΔA1B1C1 and determine its circumcentre O1. Then repeat the process once more. Connect O to O1 with a straight line.
What do you visually notice about the three circumcentres O, O1, O2 and the centroid G? Check by dragging the red vertices A, B or C. Can you make a conjecture? Can you prove or disprove your conjecture?

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Investigating circumcentres of iterated median triangles

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By Michael de Villiers. Created, 18 May 2014.