In a triangle ABC each side has been extended by it's length, we mark the edges of the segments D,E,F and draw the triangle DEF. Image What is the ratio of the areas between the two triangles. Edit: I try to draw it on geogebra and found out it's 1:7 but I have no idea how to prove it.
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1Even if it is an equilateral triangle, it is the same question because a ratio of areas is invariant by an affine transformation and it is always possible to transform any triangle into an equilateral triangle by an affine transform. – Jean Marie Apr 18 '23 at 18:18
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See also on Wikipedia – Jean Marie Apr 18 '23 at 18:21