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

`#include<time.h>`

`#include<stdlib.h>`

`#include<iostream>`

`#include<math.h>`

using namespace std;

const int LOW = 0;

const int HIGH = 10;

int main(int argc, char **argv)

`{`

time_t seconds;

time(&seconds);

srand((unsigned int) seconds);

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

double m1, m2, c1, c2, r;

x1 = rand() % (HIGH - LOW + 1) + LOW;

x2 = rand() % (HIGH - LOW + 1) + LOW;

x3 = rand() % (HIGH - LOW + 1) + LOW;

y1 = rand() % (HIGH - LOW + 1) + LOW;

y2 = rand() % (HIGH - LOW + 1) + LOW;

y3 = rand() % (HIGH - LOW + 1) + LOW;

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

cout << "The points on the circle are: (" << x1 << ", " << y1 << "), ("

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

cout << "\nThe center of the circle is (" << c1 << ", " << c2

<< ") and radius is " << r;

cout << "\nEnter the point : <x>,<y>";

int x, y;

cin >> x;

cin >> y;

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

if (s < 0)

cout << "\nThe point lies inside the circle";

else if (s > 0)

cout << "\nThe point lies outside the circle";

`else`

cout << "\nThe point lies on the circle";

return 0;

`}`

Output:

$ g++ PointWRTCircle.cpp $ a.out The points on the circle are: (2, 5), (10, 8), (3, 6) The center of the circle is (8.7, 13.7) and radius is 9.58019 Enter the point : <x>,<y> 1 2 The point lies outside the circle The points on the circle are: (0, 6), (9, 7), (6, 10) The center of the circle is (4.6, 7.4) and radius is 2.95296 Enter the point : <x>,<y>6 5 The point lies inside the circle ------------------ (program exited with code: 0) Press return to continue

**Sanfoundry Global Education & Learning Series – 1000 C++ Programs.**

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