There could be several points along the the line within a 100 feet buffer and a tolerance gap of 30 feet between point is required. Assume that there will be no more than 3 points within the buffer.
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Extract the angle of the line at this point and move it (create a point) at the required distance and angle.
Using a affiner you enter
dX=@Evaluate(-/+@Value(OFFSET)*@cos((@Value(DirectionalAngle)/180)*$(Pi ())))
dY=@Evaluate(-/+@Value(OFFSET)*@sin((@Value(DirectionalAngle)/180)*$(Pi ())))
so that would be A,B,C = 1,0,dX and D,E,F = 0,1,dY
The -/+ would indicate wich side of the line you'd be moving the point.