You need to use path.hitTest with your point, this will return a HitResult, which you can use to split the path:

var position = new Point(50, 50);
var circle = new Path.Circle(position, 5);

var splitPoint = position + new Point(5, 0);

var hitResult = circle.hitTest(splitPoint);

if(hitResult) {
	circle.split(hitResult);
	circle.segments.last.point += new Point(5, 0)
} else {
	print('The point was not on the path.');
}

ps: currently when you use a point, it returns an error - while actually it should tell you that it doesn't accept a point as a parameter. I will add this as a bug to GitHub. Also, it might be nice to have divide also accept a point as a parameter.

Thank you!

it works for what i needed.

one precision though: what does this line in your code do? circle.segments.last.point += new Point(5, 0)

well, maybe i can answer that myself.
i tried to define the points used by hitTest at random using the following code:

//FIRST CIRCLE
var xorig = Math.random()*40;
var yorig = Math.random()*40;
var orig = new Point(xorig, yorig);
var radius = Math.random()*20;
var circle0 = new Path.Circle(orig, radius);

var theta1 = Math.random();
var theta2 = Math.random();

var cos1 = Math.cos(theta1);
var sin1 = Math.sin(theta1);
var cos2 = Math.cos(theta2);
var sin2 = Math.sin(theta2);

var diffx1 = xorig + cos1*radius;
var diffy1 = yorig + sin1*radius;
var point1 = new Point(diffx1, diffy1);

var diffx2 = xorig + cos2*radius;
var diffy2 = yorig + sin2*radius;
var point2 = new Point(diffx2, diffy2);

//CUT THE CIRCLE	
var hitResult1 = circle0.hitTest(point1);
var seg1 = circle0.split(hitResult1); 
//seg1.selected=true

var hitResult2 = circle0.hitTest(point2);
var seg2 = circle0.split(hitResult2); 
var seg;

if (seg1.length>seg2.length)
	{
	seg2.remove();
	var seg = seg1;
	}
else 
	{
	seg1.remove();
	var seg = seg2;
	}

but once in a while i got a "NullPointerException" in the console. So i guess it's a matter of precision. AI (or SG?) can't be infinitely precise. So sometime the points chosen at random are not on the circle.
Am I right?

thanks!