 # C++ Programming Code Examples

## C++ > Computer Graphics Code Examples

### Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane

``` Check if a Point d lies Inside or Outside a Circle Defined by Points a, b, c in a Plane 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. #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; } ``` 