Question

I am attempting to animate a spotlight in HTML5 canvas. What I want it to look like is this:

I am stuck on finding the two points in red. Quite naively, I thought the equation for one of the points would be:

x = circleOrigin.x + circle.radius/2;
y = circleOrigin.y + circle.radius/2;

But when I move the circle around, the lines overlap the circle. Is there a better equation for these points?

Answer 1

I thought one of the answers was correct but not verbose enough:

Finding the length between the points:

var len = Math.sqrt(Math.pow(circle.x - origin.x, 2) + Math.pow(circle.y - origin.y, 2));

The point intersections:
var intersectx = circle.x + (radius*(origin.y - circle.y)/len);
var intersecty = circle.y + (radius*(circle.x - origin.x)/len);