3171. Point within a circle

Check, if the point is inside the circle.

Input. The first line contains the coordinates of the circle center and its radius. The second line contains the coordinates of point A. All numbers are integers not exceeding 10000 by absolute value.

Output. Print “YES”, if the point A belongs to a circle (with boundaries), and “NO” otherwise.

Sample input

Sample output

2 1 2

1 3

SOLUTION

geometry

Algorithm analysis

Let (x, y) be the coordinates of the center of the circle and r be its radius. Let (a, b) be the coordinates of point A. Point A lies inside the circle (including boundaries) if

(x – a)² + (y – b)² ≤ r²

Algorithm realization

Read the input data.

scanf("%d %d %d",&x,&y,&r);

scanf("%d %d",&a,&b);

Check if point (a, b) lies inside the circle.

if ((x - a)*(x - a) + (y - b)*(y - b) <= r*r)

puts("YES");

else

puts("NO");

Algorithm realization – structures

#include <stdio.h>

int x, y, r, a, b;

struct circle

{

int x, y, r;

} c;

struct point

{

int x, y;

} p;

int inside(struct point p, struct circle c)

{

return ((c.x - p.x)*(c.x - p.x) + (c.y - p.y)*(c.y - p.y) <= c.r * c.r);

}

int main(void)

{

scanf("%d %d %d", &c.x, &c.y, &c.r);

scanf("%d %d", &p.x, &p.y);

if (inside(p, c))

puts("YES");

else

puts("NO");

return 0;

}

Algorithm realization – classes

#include <stdio.h>

class Point

{

public:

double x, y;

Point(double x, double y) : x(x), y(y) {}

};

class Circle

{

public:

double x, y, r;

Circle(double x, double y, double r) : x(x), y(y), r(r) {}

int Inside(Point &p)

{

return (x - p.x)*(x - p.x) + (y - p.y)*(y - p.y) <= r * r;

}

};

double x, y, r, a, b;

int main(void)

{

scanf("%lf %lf %lf",&x,&y,&r);

Circle c(x,y,r);

scanf("%lf %lf",&a,&b);

Point p(a,b);

if (c.Inside(p)) puts("YES"); else puts("NO");

return 0;

}

Java realization

import java.util.*;

public class Main

{

public static void main(String[] args)

{

Scanner con = new Scanner(System.in);

int x = con.nextInt();

int y = con.nextInt();

int r = con.nextInt();

int a = con.nextInt();

int b = con.nextInt();

if ((x - a)*(x - a) + (y - b)*(y - b) <= r*r)

System.out.println("YES");

else

System.out.println("NO");

con.close();

}

Java realization – classes

import java.util.*;

class Point

{

int x, y;

Point(int x, int y)

{

this.x = x;

this.y = y;

}

class Circle

{

int x, y, r;

Circle(int x, int y, int r)

{