This should get you started, find where lines drawn between every other point defining the circle crosses

😎

USE tempdb;

GO

DECLARE @circle GEOMETRY = 'CIRCULARSTRING (52.6107417597068 -1.19053984363516, 52.6107417597068 -1.19185949047026, 52.6114844449159 -1.19185949047026, 52.6114844449159 -1.19053984363516, 52.6107417597068 -1.19053984363516)'

;WITH T(N) AS (SELECT X.N FROM (VALUES (NULL),(NULL),(NULL),(NULL),(NULL),(NULL),(NULL),(NULL),(NULL)) AS X(N))

,NUMS(N) AS (SELECT TOP(@CIRCLE.STNumPoints() - 1 ) ROW_NUMBER() OVER (ORDER BY (SELECT NULL)) AS N FROM T T1,T,T T2,T T3,T T4)

,C_POINTS AS

(

SELECT

NM.N AS POINT_NO

,@CIRCLE.STPointN(N) /*.STBuffer(0.0001)*/ AS POINT_GEO

FROM NUMS NM

)

SELECT

C1.POINT_GEO.ShortestLineTo(C3.POINT_GEO).STIntersection(C2.POINT_GEO.ShortestLineTo(C4.POINT_GEO)).STBuffer(0.0001)

FROM C_POINTS C1

CROSS APPLY C_POINTS C2

CROSS APPLY C_POINTS C3

CROSS APPLY C_POINTS C4

WHERE C1.POINT_NO = 1

AND C2.POINT_NO = 2

AND C3.POINT_NO = 3

AND C4.POINT_NO = 4

UNION ALL

SELECT @circle