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enter image description here

Three equilateral triangles with side lengths 28 are placed in the position as shown in the picture above. All the contacts are perfect and a circle passes by exactly one vertex per triangle. What’s the minimal radius?

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  • $\begingroup$ Does this have a neat, puzzle-like solution? $\endgroup$ – Dr Xorile May 27 at 22:11
  • $\begingroup$ Yes, it does have one $\endgroup$ – Display maths May 27 at 22:30
4
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So I believe the radius is:

$84\left(\sqrt{3}-\sqrt{2}\right)\approx26.69832$

I get this by assuming that the centre of the circle is $x$ along the line between the two joined triangles on the right, and that the apex of the triangle on the left is horizontal with this, which I think is correct. Solve for $x$ here. And substitute back to get the radius here.

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  • $\begingroup$ I’m sorry, but the answer is incorrect. $\endgroup$ – Display maths May 27 at 22:29
  • $\begingroup$ Okay, I fixed it. Was not thinking clearly... $\endgroup$ – Dr Xorile May 27 at 23:09
  • $\begingroup$ Yeah, this is the good answer! Thanks! $\endgroup$ – Display maths May 27 at 23:12

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