/* Given a circle of an input radius whose center is at point 0,0, we input an x,y coordinate
 * from the user and determine if that coordinate lies on the circle, inside it or outside it.
 * We need to compute the distance from 0,0 to x,y and compare it to radius.  But given that
 * we are dealing with doubles, to lie on the circle itself we need a small error amount for
 * loss of precision so we say that the point lies on the circle if the distance - radius is
 * less than some small value, EPSILON */

import java.util.Scanner;

public class Ch4_Circle_Point
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		System.out.print("Enter the radius of your circle  ");				// input the radius, x and y all as doubles
		double radius = in.nextDouble();
		System.out.print("Enter the x-coordinate of a point  ");
		double x = in.nextDouble();
		System.out.print("Enter the y-coordinate of a point  ");
		double y = in.nextDouble();
		final double EPSILON = 0.0000001;						// use this for possible loss of precision
		double distance = Math.sqrt(x*x + y*y);					// the distance from x,y to the center, at 0,0
		if(Math.abs(distance-radius)<EPSILON) 					// is the distance from 0,0 to x,y roughly equal to the radius?
			System.out.println("The point " + x + "," + y + " lies on the circle");
		else if(distance-radius < 0)							// otherwise if the distance is less than the radius, the point lies
			System.out.println("The point " + x + "," + y + " lies inside the circle");		// inside the circle
		else System.out.println("The point " + x + "," + y + " lies outside the circle");	// otherwise it lies outside the circle
	}
}