PHP Exercises: Compute the radius and the central coordinate of a circle

Last update on May 27 2025 13:08:43 (UTC/GMT +8 hours)

53. Circle Through 3 Points

Write a PHP program to compute the radius and the central coordinate (x, y) of a circle which is constructed by three given points on the plane surface.

Sample Solution:

PHP Code:

<?php
// Define the coordinates of three points
$x1 = 0; $y1 = 0; $x2 = 2; $y2 = 0; $x3 = 2; $y3 = 2;

// Calculate coefficients for the equations of two perpendicular bisectors
$a1 = 2 * ($x2 - $x1);
$b1 = 2 * ($y2 - $y1);
$c1 = $x1 * $x1 - $x2 * $x2 + $y1 * $y1 - $y2 * $y2;

$a2 = 2 * ($x3 - $x1);
$b2 = 2 * ($y3 - $y1);
$c2 = $x1 * $x1 - $x3 * $x3 + $y1 * $y1 - $y3 * $y3;

// Calculate the coordinates of the center (x, y) and the radius (r) of the circle
$x = ($b1 * $c2 - $b2 * $c1) / ($a1 * $b2 - $a2 * $b1);
$y = ($c1 * $a2 - $c2 * $a1) / ($a1 * $b2 - $a2 * $b1);
$r = sqrt(($x - $x1) * ($x - $x1) + ($y - $y1) * ($y - $y1));

// Print the central coordinate (x, y) and the radius of the circle
printf("Central coordinate(x, y) and radius of the circle:\n");
printf("(%.3f %.3f) %.3f\n", $x, $y, $r);

?>

Explanation:

Point Definition:

Three points are defined in a 2D space:

Point 1: (x1,y1) = (0,0)

Point 2: (x2,y2) = (2,0)

Point 3: (x3,y3) = (2,2)

Calculate Coefficients for Perpendicular Bisectors:

Coefficients for the equations of two perpendicular bisectors are calculated using the coordinates of the points:

Calculate Center Coordinates and Radius:

The coordinates of the center of the circle (x,y) and the radius r are calculated using the coefficients:

Output the Result:

The central coordinates (x,y) and the radius r of the circle are printed:

printf("Central coordinate(x, y) and radius of the circle:\n");

printf("(%.3f %.3f) %.3f\n", $x, $y, $r); displays the values rounded to three decimal places.

Output:

Central coordinate(x,y) and radius of the circle: (1.000 1.000) 1.414

Flowchart:

For more Practice: Solve these Related Problems:

Write a PHP script to calculate the center and radius of a circle passing through three non-collinear points.

Write a PHP function to compute circle parameters from three coordinate points using circumcenter formulas.

Write a PHP script to validate three input points and derive the central coordinate and radius of the circle.

Write a PHP script to solve circle geometry using matrix operations from three given points.

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