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Five Circle Theorem
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<iframe 
    src="https://jsxgraph.uni-bayreuth.de/share/iframe/five-circle-theorem" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Five Circle Theorem" 
    allowfullscreen
></iframe>
This code has to
<div id="board-0-wrapper" class="jxgbox-wrapper " style="width: 100%; ">
   <div id="board-0" class="jxgbox" style="aspect-ratio: 1 / 1; width: 100%;" data-ar="1 / 1"></div>
</div>

<script type = "text/javascript"> 
    /*
    This example is licensed under a 
    Creative Commons Attribution 4.0 International License.
    https://creativecommons.org/licenses/by/4.0/
    
    Please note you have to mention 
    The Center of Mobile Learning with Digital Technology
    in the credits.
    */
    
    const BOARDID = 'board-0';

    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5]
    });
    var p = [], l = [], i = [], c = [], j = [], k, cc;
    
    // Blue points
    var attr = {
        name: '',
        color: '#7355ff'
    };
    p[0] = board.create('point', [-2.5, -3], attr);
    p[1] = board.create('point', [-0, 4], attr);
    p[2] = board.create('point', [2.5, -3], attr);
    p[3] = board.create('point', [-4, 0], attr);
    p[4] = board.create('point', [4, 0], attr);
    
    for (k = 0; k < 5; k++) {
        l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
    }
    
    // Intersection points: yellow
    for (k = 0; k < 5; k++) {
        i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
    }
    
    for (k = 0; k < 5; k++) {
        c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
            strokeColor: 'gray', strokeWidth: 1, 
            point: {
                visible: false
            }
        });
    }
    
    // Intersection points: red
    for (k = 0; k < 5; k++) {
        j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
    }
    
    // 6th circle: circumcircle
    cc = board.create('circumcircle', [j[0], j[2], j[3]], {
        strokeColor: 'red',
        strokeWidth: 2,
        point: {
            strokeColor: '#000000',
            fillColor: '#000000',
            size: 1
        }
    });
 </script> 
/*
This example is licensed under a 
Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/

Please note you have to mention 
The Center of Mobile Learning with Digital Technology
in the credits.
*/

const BOARDID = 'your_div_id'; // Insert your id here!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;

// Blue points
var attr = {
    name: '',
    color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);

for (k = 0; k < 5; k++) {
    l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}

// Intersection points: yellow
for (k = 0; k < 5; k++) {
    i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}

for (k = 0; k < 5; k++) {
    c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
        strokeColor: 'gray', strokeWidth: 1, 
        point: {
            visible: false
        }
    });
}

// Intersection points: red
for (k = 0; k < 5; k++) {
    j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}

// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
    strokeColor: 'red',
    strokeWidth: 2,
    point: {
        strokeColor: '#000000',
        fillColor: '#000000',
        size: 1
    }
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Five Circle Theorem" description="This construction was copied from JSXGraph examples database: BTW HERE SHOULD BE A GENERATED LINKuseGlobalJS="false">
   /*
   This example is licensed under a 
   Creative Commons Attribution 4.0 International License.
   https://creativecommons.org/licenses/by/4.0/
   
   Please note you have to mention 
   The Center of Mobile Learning with Digital Technology
   in the credits.
   */
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5]
   });
   var p = [], l = [], i = [], c = [], j = [], k, cc;
   
   // Blue points
   var attr = {
       name: '',
       color: '#7355ff'
   };
   p[0] = board.create('point', [-2.5, -3], attr);
   p[1] = board.create('point', [-0, 4], attr);
   p[2] = board.create('point', [2.5, -3], attr);
   p[3] = board.create('point', [-4, 0], attr);
   p[4] = board.create('point', [4, 0], attr);
   
   for (k = 0; k < 5; k++) {
       l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
   }
   
   // Intersection points: yellow
   for (k = 0; k < 5; k++) {
       i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
   }
   
   for (k = 0; k < 5; k++) {
       c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
           strokeColor: 'gray', strokeWidth: 1, 
           point: {
               visible: false
           }
       });
   }
   
   // Intersection points: red
   for (k = 0; k < 5; k++) {
       j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
   }
   
   // 6th circle: circumcircle
   cc = board.create('circumcircle', [j[0], j[2], j[3]], {
       strokeColor: 'red',
       strokeWidth: 2,
       point: {
           strokeColor: '#000000',
           fillColor: '#000000',
           size: 1
       }
   });
</jsxgraph>

Five Circle Theorem

// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;

// Blue points
var attr = {
    name: '',
    color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);

for (k = 0; k < 5; k++) {
    l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}

// Intersection points: yellow
for (k = 0; k < 5; k++) {
    i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}

for (k = 0; k < 5; k++) {
    c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
        strokeColor: 'gray', strokeWidth: 1, 
        point: {
            visible: false
        }
    });
}

// Intersection points: red
for (k = 0; k < 5; k++) {
    j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}

// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
    strokeColor: 'red',
    strokeWidth: 2,
    point: {
        strokeColor: '#000000',
        fillColor: '#000000',
        size: 1
    }
});

license

This example is licensed under a Creative Commons Attribution 4.0 International License.
Please note you have to mention The Center of Mobile Learning with Digital Technology in the credits.