Maybe this will work for you.
circledStar =
Module[{blue, thick, circle, pentagonPts, innerPt, starPts, star},
blue = RGBColor[{.3, .6, 1}];
thick = Scaled[.03];
circle = {Thickness[thick], Red, Circle[{0, 0}, 1.07]};
pentagonPts = CirclePoints[5];
innerPt =
RegionIntersection[
Line[{pentagonPts[[1]], pentagonPts[[3]]}],
Line[{pentagonPts[[2]], pentagonPts[[4]]}]];
starPts =
N[
DeleteDuplicates[
Catenate[
NestList[
RotationTransform[360/5 Degree],
{pentagonPts[[2]], innerPt[[1, 1]], pentagonPts[[3]]},
4]]]];
star = {EdgeForm[{Thickness[thick], Red}], FaceForm[blue], Polygon[starPts]};
Graphics[{circle, star}]]

Grid[
{{"", "first column"},
{"first row", GraphicsGrid[ConstantArray[circledStar, {2, 2}]]}},
Frame -> All]

Note
If what I did above to generate the star isn't clear to you, consider the following graphic.
Module[{thick, pentagonPts, innerPt, starPart},
thick = Scaled[.03];
pentagonPts = CirclePoints[5];
innerPt =
RegionIntersection[
Line[{pentagonPts[[1]], pentagonPts[[3]]}],
Line[{pentagonPts[[2]], pentagonPts[[4]]}]];
starPart = Line[{pentagonPts[[2]], innerPt[[1, 1]], pentagonPts[[3]]}];
Graphics[
{Thickness[thick], Red, starPart,
Text[Style["innerPt", 14, Black], innerPt[[1, 1]], {0, 2}],,
MapThread[Text[Style[#1, 20, Black], #2] &, {Range[5], pentagonPts}]}]]

Here you see the five vertices of a pentagon labeled 1 through 5. In the code I found the intersection of the line from 1 to 3 with the line from 2 to 4. Then I constructed one fifth of the star from points 2 and 3 and innerPt
, the found intersection.
In the main graphic. I took this set of tree points, rotated it trough 105 degrees about the origin, rotated the results trough 105 degrees again, and so on until I had five sets of three points. I deleted the duplicates and made a flat list of remaining points, which form the vertices of the star polygon in the main graphic.