It's a little confusing what you need to do. In this case you have to be aware of what's happening internally within Inventor when you add the coincident constraint. It's not actually adding a new constraint but is changing the entities so that they share a single sketch point.
The code below demonstrates two different approaches to get the same result. One is to create the initial sketch entities entirely independent of each other and then connect that points after. The code does this below to connect the two lines to the circle center by using the Merge method on the SketchPoint object. The second approach, and the one I prefer is to create then connected. The code below demonsrates this when it's creating the arc. Instead of defining the start point of the arc using X,Y coordinates it provides the center sketch point of the circle. This does two things. First it defines the position and it will also create the line such that it's uses that sketch point as it's starting point.
Public Sub SketchConstraints()
Dim partDoc As PartDocument
Set partDoc = ThisApplication.ActiveDocument
Dim sketch As PlanarSketch
Set sketch = partDoc.ComponentDefinition.Sketches.Add( _
partDoc.ComponentDefinition.WorkPlanes.Item(3))
Dim tg As TransientGeometry
Set tg = ThisApplication.TransientGeometry
Dim line1 As SketchLine
Dim line2 As SketchLine
Dim circ As SketchCircle
Dim arc As SketchArc
Set circ = sketch.SketchCircles.AddByCenterRadius( _
tg.CreatePoint2d(0, 0), 5)
Set line1 = sketch.SketchLines.AddByTwoPoints( _
tg.CreatePoint2d(1, 1), _
tg.CreatePoint2d(6, 6))
Set line2 = sketch.SketchLines.AddByTwoPoints( _
tg.CreatePoint2d(-1, 1), _
tg.CreatePoint2d(-6, 6))
Set arc = sketch.SketchArcs.AddByThreePoints( _
circ.CenterSketchPoint, _
tg.CreatePoint2d(1, -3), _
tg.CreatePoint2d(4, -4))
Call circ.CenterSketchPoint.Merge(line1.StartSketchPoint)
Call circ.CenterSketchPoint.Merge(line2.StartSketchPoint)
sketch.Solve
End Sub