Graphics[{{Yellow, #}, {Green, Circle /@ #[[1]]}}] &@
  SSSTriangle[1, 1, 1]

pts = CirclePoints[3]
Graphics[{
  Thick, Green, Circle[#, Sqrt[3]] & /@ pts,
  Yellow, EdgeForm[Black],
  FilledCurve@Line@pts
}]

circles = {Circle[{-1/2, 0}, 1], Circle[{1/2, 0}, 1]};
AppendTo[circles,
  Circle[RegionIntersection[circles] // First // Last, 1]];
triangle = (RegionIntersection[#1, #2, Disk @@ #3] &) @@@
           (RotateRight[circles, #] & /@ Range[3]) // Part[#, All, 1] & // Polygon;
Graphics[{Green, circles, Yellow, EdgeForm[Black], triangle}]

Graphics[{Green, {Circle[{-(1/2), 0}, 1], Circle[{1/2, 0}, 1],
   Circle[{0, Sqrt[3]/2}, 1]}, Yellow, EdgeForm[Black],
  Polygon[{{1/2, 0}, {-(1/2), 0}, {0, Sqrt[3]/2}}]}]

scene = GeometricScene[
    {a, b, c}, (* points *)
    {
    Triangle[{a, b, c}],
    CircleThrough[{a, b}, c],
    CircleThrough[{b, c}, a],
    CircleThrough[{c, a}, b]
    }
];
scene //RandomInstance

FindGeometricConjectures[scene]["Conclusions"]