Finding point

How can I find the two points marked in the image by the green dots?
I know all the other points marked by crosses in the image.

Here is the test code for the scene. I'm a bit stumped on how to go about solving for these position points.

Thanks

[code]
delete objects
startPoint = [3.0,5.196,0.0]
endPoint = [0.0,12.0,0.0]
orgPointA = [0,10.5,0]
orgPointB= [0,8,0]

point pos:startPoint size:.5 wirecolor:yellow
point pos:endPoint size:.5 wirecolor:yellow
Arc radius:orgPointA.y from:0 to:90 pie:off reverse:off pos:[0,0,0] wirecolor:red
Arc radius:orgPointB.y from:0 to:90 pie:off reverse:off pos:[0,0,0] wirecolor:red
sp = splineshape wirecolor:red
spIndex = addNewSpline sp
addKnot sp spIndex #smooth #curve startPoint
addKnot sp spIndex #smooth #curve endPoint
updateshape sp
orgPtA = point pos:orgPointA size:.5 wirecolor:Green
orgPtB = point pos:orgPointB size:.5 wirecolor:Green