A triangle has sides a,b,c and the medians d,e,f ending at those sides, respectively. Given the lengths (a,b,f) construct the triangle. (Start with a triangle with side lengths determined in some manor from the given 3 lengths.)

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## Solution

I would start with 2f at the base and add the sides a,b then slide a along b and b along a to make a parallelogram (or rotate the triangle around center of 2f) Then join the vertices at (a,b) to make the side c. Apollonius would be proud!