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Circle inversion
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<iframe 
    src="https://www.jsxgraph.org/share/iframe/circle-inversion" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Circle inversion" 
    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';

    var board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        showClearTraces: true
    });
    var m = board.create('point', [0.5, 0.3], {
        name: 'M'
    });
    var b = board.create('point', [3, 0]);
    var c = board.create('circle', [m, b], {
        strokeColor: 'black',
        name: 'c'
    });
    var m1 = board.create('point', [-4, 2], {
        name: 'M_1'
    });
    var b1 = board.create('point', [-4, 3], {
        name: 'C_1'
    });
    var c1 = board.create('circle', [m1, b1]);
    var p = board.create('glider', [-4, 1, c1], {
        name: 'P [drag me]'
    });
    
    var t = board.create('polar', [c, p], {
        name: 'polar',
        withLabel: true,
        strokeColor: 'blue',
        dash: 2
    });
    var l = board.create('line', [m, p], {
        name: '',
        withLabel: false,
        strokeColor: 'gray',
        dash: 2
    });
    var s = board.create('intersection', [l, t, 0], {
        name: "P'",
        withLabel: true,
        trace: true
    });
 </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!

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    showClearTraces: true
});
var m = board.create('point', [0.5, 0.3], {
    name: 'M'
});
var b = board.create('point', [3, 0]);
var c = board.create('circle', [m, b], {
    strokeColor: 'black',
    name: 'c'
});
var m1 = board.create('point', [-4, 2], {
    name: 'M_1'
});
var b1 = board.create('point', [-4, 3], {
    name: 'C_1'
});
var c1 = board.create('circle', [m1, b1]);
var p = board.create('glider', [-4, 1, c1], {
    name: 'P [drag me]'
});

var t = board.create('polar', [c, p], {
    name: 'polar',
    withLabel: true,
    strokeColor: 'blue',
    dash: 2
});
var l = board.create('line', [m, p], {
    name: '',
    withLabel: false,
    strokeColor: 'gray',
    dash: 2
});
var s = board.create('intersection', [l, t, 0], {
    name: "P'",
    withLabel: true,
    trace: true
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Circle inversion" 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.
   */
   
   var board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       showClearTraces: true
   });
   var m = board.create('point', [0.5, 0.3], {
       name: 'M'
   });
   var b = board.create('point', [3, 0]);
   var c = board.create('circle', [m, b], {
       strokeColor: 'black',
       name: 'c'
   });
   var m1 = board.create('point', [-4, 2], {
       name: 'M_1'
   });
   var b1 = board.create('point', [-4, 3], {
       name: 'C_1'
   });
   var c1 = board.create('circle', [m1, b1]);
   var p = board.create('glider', [-4, 1, c1], {
       name: 'P [drag me]'
   });
   
   var t = board.create('polar', [c, p], {
       name: 'polar',
       withLabel: true,
       strokeColor: 'blue',
       dash: 2
   });
   var l = board.create('line', [m, p], {
       name: '',
       withLabel: false,
       strokeColor: 'gray',
       dash: 2
   });
   var s = board.create('intersection', [l, t, 0], {
       name: "P'",
       withLabel: true,
       trace: true
   });
</jsxgraph>
The point $P′$ is the result of a circle inversion of point $P$ on circle $c$ (black circle line). The *polar* of $P$ and $c$ is the dashed blue line The intersection points of the polar with the circle determine the two lines through $P$ which are tangent to $c$.
// Define the id of your board in BOARDID

var board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    showClearTraces: true
});
var m = board.create('point', [0.5, 0.3], {
    name: 'M'
});
var b = board.create('point', [3, 0]);
var c = board.create('circle', [m, b], {
    strokeColor: 'black',
    name: 'c'
});
var m1 = board.create('point', [-4, 2], {
    name: 'M_1'
});
var b1 = board.create('point', [-4, 3], {
    name: 'C_1'
});
var c1 = board.create('circle', [m1, b1]);
var p = board.create('glider', [-4, 1, c1], {
    name: 'P [drag me]'
});

var t = board.create('polar', [c, p], {
    name: 'polar',
    withLabel: true,
    strokeColor: 'blue',
    dash: 2
});
var l = board.create('line', [m, p], {
    name: '',
    withLabel: false,
    strokeColor: 'gray',
    dash: 2
});
var s = board.create('intersection', [l, t, 0], {
    name: "P'",
    withLabel: true,
    trace: true
});

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.