Euclid's Muse

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A triangle from medians

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Phil Todd



AD, BE and CF are medians of the triangle ABC.

Triangle GHI has GH=BE, HI=CF and GI=AD.

HL, IJ and GK are medians of GHI.

What is the relationship between the length of these medians and the lengths of the sides of ABC?

Can you prove this relationship geometrically?

Tags: triangle, median
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