double left  = //rectangle's most left coordinate
double bottom = //rectangle's most bottom coordinate
//etc
double centerX = //player (circle) center X coordinate
double centerY //it's y coord
double radius //radius of the circle

if(((left-centerX)*(left-centerX)+(bottom-centerY)*(bottom-centerY))<radius){
//it is intersecting
}

double r0 //radius of player
double r1 //radius of shape
double x0 //center X of player
double x1 //center X of shape
double y0 //center Y of player
double y1 //center Y of shape

double DX = x1 - x0;
double DY = y1 - y0;
double D = Math.hypot(DX, DY);
if(D<r0+r1){
//They are intersecting
}