Why doesn't CGPathIsRect work? Why doesn't CGPathContainsPoint work?

Question

I am making a CGPoint and a CGPathRef then trying to find if the CGPoint is inside the CGPathRef. Here is the code:

CGMutablePathRef path = CGPathCreateMutable();
CGPathMoveToPoint(path, NULL, 0, 0);
CGPathMoveToPoint(path, NULL, 200, 0);
CGPathMoveToPoint(path, NULL, 200, 200);
CGPathMoveToPoint(path, NULL, 0, 200);
CGPathCloseSubpath(path);

CGPoint hitPoint = CGPointMake(77, 77);

if ( CGPathIsEmpty(path) )
    NSLog(@"Path Is Empty!");
else
{
    if ( CGPathIsRect(path, NULL) ) 
        NSLog(@"Path is a Rectangle!");
    else
    {
        NSLog(@"Path is NOT a Rectangle!");
        if (CGPathContainsPoint(path, NULL, hitPoint, FALSE)) // FALSE or TRUE - same result
            NSLog(@"Hit Point Inside: x=%f, y=%f", hitPoint.x, hitPoint.y);
        else
            NSLog(@"Hit Point Outside: x=%f, y=%f", hitPoint.x, hitPoint.y);
    }
}    

The output reads:

Path is NOT a Rectangle!
Hit Point Outside: x=77.000000, y=77.000000

The path obviously is a rectangle and the point is inside the closed path. Please clue me in on what I am doing wrong here.