# Intersection of 3 circles in GeometricScene

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.

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

• Excellent - works like a dream. I would upvote you but don't have enough kudos, unfortunately. Thank you very much for this, great answer! Commented Jun 28, 2020 at 12:24
• @SorinS You're welcome! I've just done what I can. Commented Jun 28, 2020 at 12:38
• @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. Commented Jun 28, 2020 at 15:48
• Hi Marco - thank you for your comment, I went ahead and upvoted and also accepted @SneezeFor16Min answer. Commented Jul 3, 2020 at 17:37