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Fill the intersection area of two circles
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<iframe 
    src="http://jsxgraph.org/share/iframe/fill-the-intersection-area-of-two-circles" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Fill the intersection area of two circles" 
    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: [-1, 5, 5, -1],
        axis: true
    });
    
    // Create two circles
    var p1 = board.create('point', [1, 1]);
    var p2 = board.create('point', [3, 0]);
    var c1 = board.create('circle', [p1, p2], {strokeWidth:1});
    
    var p3 = board.create('point', [4, 1]);
    var p4 = board.create('point', [2, 0]);
    var c2 = board.create('circle', [p3, p4], {strokeWidth:1});
    
    // Intersecting curve
    var a = board.create('curveintersection', [c1, c2], {
        strokeColor: 'red', 
        strokeWidth:3, 
        fillColor: 'yellow',
        fillOpacity: 0.3,
        highlightFillColor: 'blue',
        highlightFillOpacity: 0.3,
        hasInnerPoints: 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!

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-1, 5, 5, -1],
    axis: true
});

// Create two circles
var p1 = board.create('point', [1, 1]);
var p2 = board.create('point', [3, 0]);
var c1 = board.create('circle', [p1, p2], {strokeWidth:1});

var p3 = board.create('point', [4, 1]);
var p4 = board.create('point', [2, 0]);
var c2 = board.create('circle', [p3, p4], {strokeWidth:1});

// Intersecting curve
var a = board.create('curveintersection', [c1, c2], {
    strokeColor: 'red', 
    strokeWidth:3, 
    fillColor: 'yellow',
    fillOpacity: 0.3,
    highlightFillColor: 'blue',
    highlightFillOpacity: 0.3,
    hasInnerPoints: true
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Fill the intersection area of two circles" 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: [-1, 5, 5, -1],
       axis: true
   });
   
   // Create two circles
   var p1 = board.create('point', [1, 1]);
   var p2 = board.create('point', [3, 0]);
   var c1 = board.create('circle', [p1, p2], {strokeWidth:1});
   
   var p3 = board.create('point', [4, 1]);
   var p4 = board.create('point', [2, 0]);
   var c2 = board.create('circle', [p3, p4], {strokeWidth:1});
   
   // Intersecting curve
   var a = board.create('curveintersection', [c1, c2], {
       strokeColor: 'red', 
       strokeWidth:3, 
       fillColor: 'yellow',
       fillOpacity: 0.3,
       highlightFillColor: 'blue',
       highlightFillOpacity: 0.3,
       hasInnerPoints: true
   });
</jsxgraph>

Fill the intersection area of two circles

Circles
Curves
Intersection, Union, Difference
Have also a look at the examples 
// Define the id of your board in BOARDID

const board = JXG.JSXGraph.initBoard(BOARDID, {
    boundingbox: [-1, 5, 5, -1],
    axis: true
});

// Create two circles
var p1 = board.create('point', [1, 1]);
var p2 = board.create('point', [3, 0]);
var c1 = board.create('circle', [p1, p2], {strokeWidth:1});

var p3 = board.create('point', [4, 1]);
var p4 = board.create('point', [2, 0]);
var c2 = board.create('circle', [p3, p4], {strokeWidth:1});

// Intersecting curve
var a = board.create('curveintersection', [c1, c2], {
    strokeColor: 'red', 
    strokeWidth:3, 
    fillColor: 'yellow',
    fillOpacity: 0.3,
    highlightFillColor: 'blue',
    highlightFillOpacity: 0.3,
    hasInnerPoints: 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.