Erased triangle

I draw an equilateral triangle on the sand. On each side I put a stone.
Two days later, the stones are still there, but the wind has blown away the triangle.
Could you find again the triangle from the stone ?
Of course not ! there are infinitely many ! But find the largest one ? Solution

Extensions

Now I put the stones on the lines containing the sides.
Same problem. Solution

Circles

Replace points by circles, that is to construct the largest equilateral triangle whose sides are tangent to three given circles, just one circle per side of course.

Details

 

 

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