How to constrain a point outside of a circle to the circles edge

[serial]

Basically I want to be able to move my mouse and have the XY coordinates stay relative to a circle. 

Just curious if anybody has any info on the math behind this.

[Mithrandir_]

So what you are asking is that if your cursor is outside of the circle and you draw a line from the cursor position to the center of the circle, then the intersection between the circle and line is what you are after. Correct?