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.

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