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 ?
Now I put the stones on the lines
containing the sides.
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.