[ Edited to fix a typo and an omission ]
Here's how to hit-test a rectangle and a circle for collision:
Demo: http://jsfiddle.net/m1erickson/n6U8D/
var circle={x:100,y:290,r:10};
var rect={x:100,y:100,w:40,h:100};
// return true if the rectangle and circle are colliding
function RectCircleColliding(circle,rect){
var distX = Math.abs(circle.x - rect.x-rect.w/2);
var distY = Math.abs(circle.y - rect.y-rect.h/2);
if (distX > (rect.w/2 + circle.r)) { return false; }
if (distY > (rect.h/2 + circle.r)) { return false; }
if (distX <= (rect.w/2)) { return true; }
if (distY <= (rect.h/2)) { return true; }
var dx=distX-rect.w/2;
var dy=distY-rect.h/2;
return (dx*dx+dy*dy<=(circle.r*circle.r));
}
[Added answer given clarification]
...And this is how to test if the circle is completely contained in the rectangle
Demo: http://jsfiddle.net/m1erickson/VhGcT/
// return true if the circle is inside the rectangle
function CircleInsideRect(circle,rect){
return(
circle.x-circle.r>rect.x &&
circle.x+circle.r<rect.x+rect.w &&
circle.y-circle.r>rect.y &&
circle.y+circle.r<rect.y+rect.h
)
}
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