How can I draw intersection of a sphere and a plane?

Question

In this code, how can I draw the circle is intersection of the plane A1A2A3 and sphere?

Clear["Global`*"];
n = 8;
a = 2;
b = 6;
R = a/(2 Sin[Pi/n]);
h = Sqrt[b^2 - R^2];
verticesBase = 
  Table[{R Cos[2 Pi k/n], R Sin[2 Pi k/n], 0}, {k, 0, n - 1}];
vertexTop = {0, 0, h};
circumsphere = 
  Circumsphere[{vertexTop, verticesBase[[1]], verticesBase[[2]], 
    verticesBase[[3]]}];
Graphics3D[{Opacity[0.6], LightOrange, EdgeForm[{Black, Thin}], 
  Table[Polygon[{verticesBase[[k]], verticesBase[[Mod[k, n] + 1]], 
     vertexTop}], {k, 1, n}], Yellow, Polygon[verticesBase], 
  Text[Style["S", 14, Bold, Black], vertexTop + {0, 0, 0.2}], 
  Table[Text[Style["A" <> ToString[k], 14, Bold, Black], 
    verticesBase[[k]] + {0, 0, -0.2}], {k, 1, n}], Opacity[0.4], 
  LightOrange, Sphere[circumsphere[[1]], circumsphere[[2]]]}, 
 Boxed -> False, Axes -> False]

Answer 1

Region[Style[
  RegionIntersection[InfinitePlane[verticesBase[[1 ;; 3]]], 
   circumsphere], Directive@{Thick, Red}]]