Scratch

//Variables for the circle
private var circle.x=20
private var circle.y=20
private var circle.radius=10
private var circle.points=12
private var $circle.step=0
private var $circle.angle=0
//Variables for the square
private var square.x=-20
private var square.y=-20
//A square with a radius? No way!
private var square.radius=10
private var square.direction=0
//Handy dandy loop variable
private var $loop=0
//All-purpose collision variable
private var $collision="true"
//More collision variables
private var $distance=0
private var $distanceX=0
private var $distanceY=0
private var $direction=0
private var $pointX
private var $pointY
private var $greater

/*This flag click script continually broadcasts a render command. If you're adamant about keeping the project one-script as
well as one-sprite, you can combine the scripts, obviously, by placing the scripts from the "when I receive" hats in place of
the block that broadcasts them. For convenience, I break this up into several scripts.*/
when flag clicked{
    forever{
        broadcast "render" and wait
        broadcast "collisions" and wait
    }
}

when I receive "render"{
    clear;
    /*Let's draw the circle first. Circles are painful in this type of real-time rendering as they have to be drawn by the 
    individual points on the circle rather than with a "move 3 steps"/"turn 3 degrees" loop. I think we can get a decent circle
    with 12 points. Technically, we're drawing a dodecagon.*/
    pen up;
    //In Scratch, I tend to put dollar signs in front of variables that go in loops or are kind of temporary. You just don't get it.
    $circle.step=0
    $circle.angle=360/circle.points
    pen down;
    go to x: circle.x , y: circle.y+circle.radius;
    repeat (circle.points){
        change $circle.step by 1
        got to x: circle.x+(sin($circle.step*$circle.angle)*circle.radius) , y: circle.y+(cos($circle.step*$circle.angle)*circle.radius)
    }
    pen up;
    //Now let's do the square. Squares are a bit simpler. Again, you're free to break it up into more broadcasts or combine them if you like.
    $loop=0
    go to x: square.x+(sin(45+square.direction)*square.radius) , y: square.y+(sin(45+square.direction)*square.radius);
    pen down;
    repeat (3){
        change $loop by 90;
        go to x: square.x+(sin(45+square.direction+$loop)*square.radius) , y: square.y+(sin(45+square.direction+$loop)*square.radius);
    }
    pen up;
        
}

when I receive "collisions"{
    //Now let's check to see whether the two shapes are touching.
    if(circle.radius>square.radius){
        $greater=circle.radius
    }else{
        $greater=square.radius
    }
    if(sqrt(((square.x-circle.x)*(square.x-circle.x))+((square.y-circle.y)*(square.y-circle.y)))<$greater){
        //If the center of one object falls within the circular bounds of another, our job gets a whole lot easier.
        $collision=true
    }else{
        /*We're going to find the direction from the square to the circle.
        Picture a triangle whose hypotenuse runs from the point in the center of the circle (circle.x,circle.y) to the point in the center of the square (square.x,square.y)
        The $distanceX and $distanceY variables form the adjacent and opposite sides of the triangle and are the difference between the objects' x and y positions.*/
        $distanceX=square.x-circle.x
        $distanceY=square.y-circle.y
        //The $distance variable is the distance between the centers the two objects. 
        $distance=sqrt(((square.x-circle.x)*(square.x-circle.x))+((square.y-circle.y)*(square.y-circle.y)));
        $direction=(acos($distanceY/$distance))*($distanceX+0.001/(abs($distanceX)+0.001))
        //If for some reason this doesn't work, try changing $direction by 180 at this point.
        //Now that we know the direction, we can find the point on the circle that is closest to the square. If that falls within the square, we've got a collision.
        $pointX=circle.x+(sin($direction)*$distance)
        $pointY=circle.y+(cos($direction)*$distance)
        //All that remains to do is determine whether the square's distance to ($pointX,$pointY) is less than or equal to its outer radius.
        //I'm recycling the $distance variable, and it will now refer to the distance from (square.x,square.y) to ($pointX,$pointY)
        $distance=sqrt(((square.x-$pointX)*(square.x-$pointX))+((square.y-$pointY)*(square.y-$pointY)))
        if(not($distance>square.radius)){
            $collision=true
            say("Whoa, a collision!")
            broadcast "collision"
        }else{
            $collision=false
            say("")
        }
    }
}

when I receive "collision"{
    //Do something interesting when the objects collide.
}