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Ceva's theorem
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<iframe 
    src="http://jsxgraph.org/share/iframe/cevas-theorem" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Ceva's 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';

    JXG.Options.label.autoPosition = true;
    JXG.Options.text.fontSize = 20;
    
    const board = JXG.JSXGraph.initBoard(BOARDID, {
        boundingbox: [-5, 5, 5, -5],
        axis: false,
        showNavigation: false
    });
    
    var a = board.create('point', [-4, 0], {
        name: 'a'
    });
    var b = board.create('point', [4, -3], {
        name: 'b'
    });
    var c = board.create('point', [1, 4], {
        name: 'c'
    });
    
    var s1 = board.create('segment', [a, b], {
        color: 'black'
    });
    var s2 = board.create('segment', [a, c], {
        color: 'black'
    });
    var s3 = board.create('segment', [c, b], {
        color: 'black'
    });
    
    var as = board.create('glider', [3, 0, s3], {
        name: "a'"
    });
    var bs = board.create('glider', [4, -3, s2], {
        name: "b'"
    });
    var cs = board.create('glider', [1, 4, s1], {
        name: "c'"
    });
    
    var s4 = board.create('segment', [a, as], {
        color: 'black'
    });
    var s5 = board.create('segment', [b, bs], {
        color: 'black'
    });
    var s6 = board.create('segment', [c, cs], {
        color: 'black'
    });
    
    var TV = function(p, q, t) {
        var v = p.Dist(t) / p.Dist(q);
        if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
            return v;
        } else {
            return -v;
        }
    };
    
    var txt = board.create('text', [-4.5, -4, function() {
        return "TV(a',c,b) * TV(b',a,c) * TV(c',b,a) = " + (TV(as, c, b) * TV(bs, a, c) * TV(cs, b, a)).toFixed(2);
    }]);
 </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!

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 20;

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: false,
    showNavigation: false
});

var a = board.create('point', [-4, 0], {
    name: 'a'
});
var b = board.create('point', [4, -3], {
    name: 'b'
});
var c = board.create('point', [1, 4], {
    name: 'c'
});

var s1 = board.create('segment', [a, b], {
    color: 'black'
});
var s2 = board.create('segment', [a, c], {
    color: 'black'
});
var s3 = board.create('segment', [c, b], {
    color: 'black'
});

var as = board.create('glider', [3, 0, s3], {
    name: "a'"
});
var bs = board.create('glider', [4, -3, s2], {
    name: "b'"
});
var cs = board.create('glider', [1, 4, s1], {
    name: "c'"
});

var s4 = board.create('segment', [a, as], {
    color: 'black'
});
var s5 = board.create('segment', [b, bs], {
    color: 'black'
});
var s6 = board.create('segment', [c, cs], {
    color: 'black'
});

var TV = function(p, q, t) {
    var v = p.Dist(t) / p.Dist(q);
    if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
        return v;
    } else {
        return -v;
    }
};

var txt = board.create('text', [-4.5, -4, function() {
    return "TV(a',c,b) * TV(b',a,c) * TV(c',b,a) = " + (TV(as, c, b) * TV(bs, a, c) * TV(cs, b, a)).toFixed(2);
}]);
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Ceva's 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.
   */
   
   JXG.Options.label.autoPosition = true;
   JXG.Options.text.fontSize = 20;
   
   const board = JXG.JSXGraph.initBoard(BOARDID, {
       boundingbox: [-5, 5, 5, -5],
       axis: false,
       showNavigation: false
   });
   
   var a = board.create('point', [-4, 0], {
       name: 'a'
   });
   var b = board.create('point', [4, -3], {
       name: 'b'
   });
   var c = board.create('point', [1, 4], {
       name: 'c'
   });
   
   var s1 = board.create('segment', [a, b], {
       color: 'black'
   });
   var s2 = board.create('segment', [a, c], {
       color: 'black'
   });
   var s3 = board.create('segment', [c, b], {
       color: 'black'
   });
   
   var as = board.create('glider', [3, 0, s3], {
       name: "a'"
   });
   var bs = board.create('glider', [4, -3, s2], {
       name: "b'"
   });
   var cs = board.create('glider', [1, 4, s1], {
       name: "c'"
   });
   
   var s4 = board.create('segment', [a, as], {
       color: 'black'
   });
   var s5 = board.create('segment', [b, bs], {
       color: 'black'
   });
   var s6 = board.create('segment', [c, cs], {
       color: 'black'
   });
   
   var TV = function(p, q, t) {
       var v = p.Dist(t) / p.Dist(q);
       if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
           return v;
       } else {
           return -v;
       }
   };
   
   var txt = board.create('text', [-4.5, -4, function() {
       return "TV(a',c,b) * TV(b',a,c) * TV(c',b,a) = " + (TV(as, c, b) * TV(bs, a, c) * TV(cs, b, a)).toFixed(2);
   }]);
</jsxgraph>
$TV(a,b,c)$ is the affine / simple ratio (Teilverhältnis), i.e the signed value of $|ac|/|ab|$. If the three segments $aa'$, $bb'$, $cc'$ intersect in one common point then it follows $$ TV(a',c,b) \cdot TV(b',a,c) \cdot TV(c',b,a) = -1 $$ Depending on which affine ratios are taken this product may also be $1$.
// Define the id of your board in BOARDID

JXG.Options.label.autoPosition = true;
JXG.Options.text.fontSize = 20;

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-5, 5, 5, -5],
    axis: false,
    showNavigation: false
});

var a = board.create('point', [-4, 0], {
    name: 'a'
});
var b = board.create('point', [4, -3], {
    name: 'b'
});
var c = board.create('point', [1, 4], {
    name: 'c'
});

var s1 = board.create('segment', [a, b], {
    color: 'black'
});
var s2 = board.create('segment', [a, c], {
    color: 'black'
});
var s3 = board.create('segment', [c, b], {
    color: 'black'
});

var as = board.create('glider', [3, 0, s3], {
    name: "a'"
});
var bs = board.create('glider', [4, -3, s2], {
    name: "b'"
});
var cs = board.create('glider', [1, 4, s1], {
    name: "c'"
});

var s4 = board.create('segment', [a, as], {
    color: 'black'
});
var s5 = board.create('segment', [b, bs], {
    color: 'black'
});
var s6 = board.create('segment', [c, cs], {
    color: 'black'
});

var TV = function(p, q, t) {
    var v = p.Dist(t) / p.Dist(q);
    if (JXG.Math.Geometry.isSameDir(p.coords, q.coords, p.coords, t.coords)) {
        return v;
    } else {
        return -v;
    }
};

var txt = board.create('text', [-4.5, -4, function() {
    return "TV(a',c,b) * TV(b',a,c) * TV(c',b,a) = " + (TV(as, c, b) * TV(bs, a, c) * TV(cs, b, a)).toFixed(2);
}]);

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.