C++ Exercises: Prints the central coordinate and the radius of a circumscribed circle of a triangle

Last update on August 11 2025 12:57:02 (UTC/GMT +8 hours)

Circumscribed Circle of Triangle

Write a C++ program that prints the central coordinate and the radius of a circumscribed circle of a triangle. This circle is created from three points on the plane surface.

Visual Presentation:

C++ Exercises: Prints the central coordinate and the radius of a circumscribed circle of a triangle

Sample Solution:

C++ Code :

#include <iostream> // Including input-output stream header file
#include <iomanip> // Including input-output manipulator header file
#include <cmath> // Including math functions header file

using namespace std; // Using the standard namespace

int main() {
    // Declaring variables for coordinates and calculations
    double a, b, c, x1, y1, x2, y2, x3, y3, xp, yp, d, radius;

    // Loop to read input coordinates until the end of input
    while (cin >> x1 >> y1 >> x2 >> y2 >> x3 >> y3) {
        // Calculating lengths of the sides of the triangle formed by the coordinates
        a = sqrt((x2 - x1)*(x2 - x1) + (y2 - y1)*(y2 - y1));
        b = sqrt((x3 - x1)*(x3 - x1) + (y3 - y1)*(y3 - y1));
        c = sqrt((x3 - x2)*(x3 - x2) + (y3 - y2)*(y3 - y2));

        // Calculating the radius of the circumscribed circle using triangle sides
        radius = (a * b * c) / (sqrt((a + b + c) * (b + c - a) * (c + a - b) * (a + b - c)));

        // Calculating the coordinates of the center of the circumscribed circle (x, y)
        d = 2 * (x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2));
        xp = ((x1 * x1 + y1 * y1) * (y2 - y3) + (x2 * x2 + y2 * y2) * (y3 - y1) + (x3 * x3 + y3 * y3) * (y1 - y2)) / d;
        yp = ((x1 * x1 + y1 * y1) * (x3 - x2) + (x2 * x2 + y2 * y2) * (x1 - x3) + (x3 * x3 + y3 * y3) * (x2 - x1)) / d;

        // Outputting the coordinates and radius of the circumscribed circle
        cout << fixed << setprecision(3) << "Central coordinate of the circumscribed circle: (" << xp << ", " << yp << ")\nRadius: " << radius << endl;
    }

    return 0; // Indicating successful completion of the program
}

Sample Output:

Sample input : 6 9 7
Sample Output:
7 9 6

Flowchart:

For more Practice: Solve these Related Problems:

Write a C++ program to compute the center and radius of the circumscribed circle of a triangle given its three vertices using determinant methods.
Write a C++ program that calculates the circumscribed circle parameters and then verifies if a given point lies on the circle.
Write a C++ program to find the circumcenter of a triangle using perpendicular bisectors and then calculate the radius.
Write a C++ program that takes three points as input, computes the circumscribed circle, and displays the circle's equation.

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