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This problem is addressed in ArcGIS 8.1 Service Pack 1. See the Related Information section to download this pack.
When using the circular arc construction method ConstructBearingRadiusAngle or ConstructBearingAngleArc if a central angle of 360 degrees (6.28318530717959 radians) is used, this error is returned.
The work-around is to create a temporary line geometry that has its endpoint at the start point of the circle and use the ConstructTangentRadiusAngle constructor.
For example, assuming you are using the following line of code:
pConstCirc.ConstructBearingRadiusAngle MyStartPoint, 0, False, 42, 6.28318530717959
Dim pLn As esriCore.ILine, pPnt As esriCore.IPoint, pConstP As IConstructPoint
Set pLn = New esriCore.Line
Set pPnt = New esriCore.Point
Set pConstP = pPnt
pConstP.ConstructAngleDistance MyStartPoint, 0, 42
pLn.PutCoords MyStartPoint, pPnt
pConstCirc.ConstructTangentRadiusAngle pLn, True, False, 42, 6.28318530717959