You need to check the distance $d\leq \sqrt(Xp-Xc)^2+(Yp-Yc)^2$ from the center to the bad guy and since it has square root it's simpler to test $d^2\leq (Xp-Xc)^2+(Yp-Yc)^2\leq R^2$
$Xc$ and $Yc$ are 0 since they are in the center of circle the bad guy is in range if $(Xp)^2+(Yp)^2\leq R^2$
In some Java code it's look like this
public static Point[] internalPoints(Point[] points, double radius) {
int countPoints = 0;
for (int i = 0; i < points.length; i++) {
double xp = points[i].getX();
double yp = points[i].getY();
// points are inside the circle if d^2 <= r^2
// d^2 = (Xp-Xc)^2 + (Yp-Yc)^2
// Xp and Yp is the point that should be checked
// Xc and Xc is the point center (orgin)
// Xc and Yc are 0 you end up with d^2 = (Xp)^2 + (Yp)^2
if (xp * xp + yp * yp <= radius * radius) {
countPoints++;
}
}
int companionVar = 0;
Point[] pointsInside = new Point[countPoints];
for (int j = 0; j < countPoints; j++) {
pointsInside[companionVar] = points[j];
companionVar++;
}
return pointsInside;
}