This is a Java Program to check whether a point lies inside, outside or on the circle. For any point t (xt, yt) on the plane, its position with respect to the circle defined by 3 points (x1, y1) , (x2, y2), (x3, y3).

s = (x-xt)^2 + (y-yt)^2 – r*r

If s < 0, t lies inside the circle; if s > 0, t lies outside the circle; if s = 0, t lies on the circle.

s = (x-xt)^2 + (y-yt)^2 – r*r

If s < 0, t lies inside the circle; if s > 0, t lies outside the circle; if s = 0, t lies on the circle.

Here is the source code of the Java Program to Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.

`//This is a java program to check whether point d lies inside or outside the circle defined by a, b, c points`

import java.util.Random;

import java.util.Scanner;

public class Position_Point_WRT_Circle

`{`

public static void main(String args[])

`{`

Random random = new Random();

int x1, y1, x2, y2, x3, y3;

double m1, m2, c1, c2, r;

x1 = random.nextInt(10);

y1 = random.nextInt(10);

x2 = random.nextInt(10);

y2 = random.nextInt(10);

x3 = random.nextInt(10);

y3 = random.nextInt(10);

m1 = (y1 - y2) / (x1 - x2);

m2 = (y3 - y2) / (x3 - x2);

c1 = ((m1 * m2 * (y3 - y1)) + (m1 * (x2 + x3)) - (m2 * (x1 + x2)))

/ (2 * (m1 - m2));

c2 = ((((x1 + x2) / 2) - c1) / (-1 * m1)) + ((y1 + y2) / 2);

r = Math.sqrt(((x3 - c1) * (x3 - c1)) + ((y3 - c2) * (y3 - c2)));

System.out.println("The points on the circle are: (" + x1 + ", " + y1

+ "), (" + x2 + ", " + y2 + "), (" + x3 + ", " + y3 + ")");

System.out.println("The center of the circle is (" + c1 + ", " + c2

+ ") and radius is " + r);

System.out.println("Enter the point : <x>,<y>");

Scanner scan = new Scanner(System.in);

int x, y;

x = scan.nextInt();

y = scan.nextInt();

double s = ((x - c1) * (x - c1)) + ((y - c2) * (y - c1)) - (r * r);

if (s < 0)

System.out.println("The point lies inside the circle");

else if (s > 0)

System.out.println("The point lies outside the circle");

`else`

System.out.println("The point lies on the circle");

scan.close();

`}`

`}`

Output:

$ javac Position_Point_WRT_Circle.java $ java Position_Point_WRT_Circle The points on the circle are: (5, 9), (4, 7), (2, 0) The center of the circle is (34.5, 23.25) and radius is 39.960136386153636 Enter the point : <x>,<y> 3 5 The point lies inside the circle The points on the circle are: (0, 1), (2, 3), (5, 4) The center of the circle is (3.5, 4.5) and radius is 1.5811388300841898 Enter the point : <x>,<y> 1 2 The point lies outside the circle

**Sanfoundry Global Education & Learning Series – 1000 Java Programs.**

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