Centre and radius of a circle passing through 3 points in a plane: Difference between revisions

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 {{task}}
 Write a function which returns the centre and radius of a circle passing through three point in a plane. Demonstrate the function using the points (22.83,2.07) (14.39,30.24) and (33.65,17.31)
+=={{header|ALGOL 68}}==
+Follows the lines of the C++ code [https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/ at geeksforgeeks.org].
+<syntaxhighlight lang="algol68">
+BEGIN # find the centre and radius of a circle through 3 points                                     #
+      # follows the lines of the C++ code at                                                        #
+      # https://www.geeksforgeeks.org/equation-of-circle-when-three-points-on-the-circle-are-given/ #
+    MODE POINT  = STRUCT( REAL x, y );
+    MODE CIRCLE = STRUCT( POINT centre, REAL radius );
+    # returns the circle that passes through p1, p2 and p3                                          #
+    PROC find circle = ( POINT p1, p2, p3 )CIRCLE:
+         BEGIN
+            REAL x1 = x OF p1, y1 = y OF p1, x2 = x OF p2, y2 = y OF p2, x3 = x OF p3, y3 = y OF p3;
+            REAL x12  = x1 - x2
+               , x13  = x1 - x3
+               , y12  = y1 - y2
+               , y13  = y1 - y3
+               , y31  = y3 - y1
+               , y21  = y2 - y1
+               , x31  = x3 - x1
+               , x21  = x2 - x1
+               ;
+            REAL sx13 = x1^2 - x3^2
+               , sy13 = y1^2 - y3^2
+               , sx21 = x2^2 - x1^2
+               , sy21 = y2^2 - y1^2
+               ;
+            REAL f = ( ( ( sx13 + sy13 ) * x12 )
+                     + ( ( sx21 + sy21 ) * x13 )
+                     )
+                   / ( 2 * ( ( y31 * x12 ) - ( y21 * x13 ) ) )
+               , g = ( ( ( sx13 + sy13 ) * y12 )
+                     + ( ( sx21 + sy21 ) * y13 )
+                     )
+                   / ( 2 * ( ( x31 * y12 ) - ( x21 * y13 ) ) )
+               ;
+            REAL c = - (x1^2) - (y1^2) - ( 2 * g * x1 ) - ( 2 * f * y1 );
+            ( ( -g, -f ), sqrt( g^2 + f^2 - c ) )
+         END # find circle # ;
+    CIRCLE c = find circle( ( 22.83, 2.07 ), ( 14.39, 30.24 ), ( 33.65, 17.31 ) );
+    print( ( "Centre = ( ",   fixed( x OF centre OF c, -10, 6 ) ) );
+    print( ( ", ",            fixed( y OF centre OF c, -10, 6 ) ) );
+    print( ( " ), Radius = ", fixed(      radius OF c, -10, 6 ), newline ) )
+END
+</syntaxhighlight>
+{{out}}
+<pre>
+Centre = (  18.978516,  16.265411 ), Radius =  14.708624
+</pre>
 =={{header|BASIC}}==