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I am trying to represent the image below in Mathematica and can't seem to make it work. There doesn't seem to be any constraint of type circle intersection in the documentation. I tried this:

 GeometricScene[{{A, B, C, O, X, Y, Z}, {}}, {
       CircleThrough[{O, B, C}, X, 50],
       CircleThrough[{O, A, C}, Y, 50],
       CircleThrough[{O, A, B}, Z, 50]
  }, {}]

but the result is far from inspiring. I'm quite new to Mathematica so I might have overlooked something trivial. Any help would be great, appreciate your time.

enter image description here

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1 Answer 1

16
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You need more constraints. For example:

GeometricScene[
  {{a, b, c, o, o1, o2, o3}, {r}},
  {
   CircleThrough[{o, b, c}, o1, r],
   CircleThrough[{o, a, c}, o2, r],
   CircleThrough[{o, a, b}, o3, r],
   GeometricAssertion[{o1, o2, o3}, "Counterclockwise"],
   GeometricAssertion[{a, b, c, o}, "Distinct"],
   Equal @@
    EuclideanDistance @@@
     Subsets[{o1, o2, o3}, {2}]
  }
] // RandomInstance
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4
  • $\begingroup$ Excellent - works like a dream. I would upvote you but don't have enough kudos, unfortunately. Thank you very much for this, great answer! $\endgroup$
    – SorinS
    Jun 28, 2020 at 12:24
  • $\begingroup$ @SorinS You're welcome! I've just done what I can. $\endgroup$ Jun 28, 2020 at 12:38
  • 1
    $\begingroup$ @SorinS you now certainly have enough reputation to upvote; also remember that you can accept the answer by clicking the gray tick mark next to it if it solves your problem. $\endgroup$
    – MarcoB
    Jun 28, 2020 at 15:48
  • $\begingroup$ Hi Marco - thank you for your comment, I went ahead and upvoted and also accepted @SneezeFor16Min answer. $\endgroup$
    – SorinS
    Jul 3, 2020 at 17:37

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