This method has only one drawback, when overlaying dependencies between SketchPoint and SketchArc, the second can move. Therefore, I recommend that you lock your arches before doing this, and then unlock them if that is important to you.

Sub main
Dim oInvApp As Inventor.Application = ThisApplication
Dim oTG As TransientGeometry = oInvApp.TransientGeometry
Dim oDoc As PartDocument = ThisDoc.Document
Dim oSketch As PlanarSketch = oDoc.ComponentDefinition.Sketches(1)
oSketch.Edit()
Dim oArc1 As SketchArc = oSketch.SketchArcs(1)
Dim oArc2 As SketchArc = oSketch.SketchArcs(2)
Dim oPoint As Point2d = oTG.CreatePoint2d(0,0)
Dim oSketchPoint As SketchPoint = oSketch.SketchPoints.Add(oPoint)
Call oSketch.GeometricConstraints.AddCoincident(oSketchPoint, oArc1)
Call oSketch.GeometricConstraints.AddCoincident(oSketchPoint, oArc2)
oPoint.X = oSketchPoint.Geometry.X
oPoint.Y = oSketchPoint.Geometry.Y
Call oSketch.GeometricConstraints.AddCoincident(oArc2, ChangePointToArc(oArc1, oPoint))
Call oSketch.GeometricConstraints.AddCoincident(oArc1, ChangePointToArc(oArc2, oPoint))
oSketch.ExitEdit()
End Sub
Private Function ChangePointToArc(oArc As SketchArc, oPoint As Point2d) As SketchPoint
Dim dDist1 As Double = oArc.StartSketchPoint.Geometry.DistanceTo(oPoint)
Dim dDist2 As Double = oArc.EndSketchPoint.Geometry.DistanceTo(oPoint)
Dim oSketch As PlanarSketch = oArc.Parent
If dDist1 < dDist2 Then
oArc.StartSketchPoint.MoveTo(oPoint)
Return oArc.StartSketchPoint
Else
oArc.EndSketchPoint.MoveTo(oPoint)
Return oArc.EndSketchPoint
End If
End Function