<iframe 
    src="https://www.jsxgraph.uni-bayreuth.de/share/iframe/tangent-line-to-two-circles" 
    style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;" 
    name="JSXGraph example: Tangent lines simultaneously to two circles" 
    allowfullscreen
></iframe>

<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 ShareAlike 4.0 International License.
    https://creativecommons.org/licenses/by-sa/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: [-8, 8, 8, -8],
        keepaspectratio: true
    });
    
    // Define the two circles
    var o1 = board.create('point', [-2, 2], { name: 'O_1' });
    var o2 = board.create('point', [3, -3], { name: 'O_2' });
    
    var p1 = board.create('point', [-3, 5], { name: 'P_1' });
    var p2 = board.create('point', [2, -3], { name: 'P_2' });
    
    var c1 = board.create('circle', [o1, p1]);
    var c2 = board.create('circle', [o2, p2]);
    
    // The construction of the tangents starts here:
    var m = board.create('midpoint', [o1, o2], { name: 'M' });
    var lm = board.create('line', [o1, o2], { strokeWidth: 1, strokeColor: 'gray' });
    
    // The circle with center M containing the two centers O_1 and O_2
    var c3 = board.create('circle', [m, o2], { strokeColor: 'green', strokeWidth: 1 });
    
    var c4 = board.create('circle', [o1, () => Math.abs(c1.Radius() - c2.Radius())], {
        strokeColor: 'purple',
        strokeWidth: 1
    });
    
    var i1 = board.create('intersection', [c3, c4, 0], { visible: true });
    var i2 = board.create('intersection', [c3, c4, 1], { visible: true });
    
    var l1 = board.create('line', [o1, i1], { visible: false });
    var l2 = board.create('line', [o1, i2], { visible: false });
    
    var i3 = board.create('intersection', [c1, l1, 0]);
    var i4 = board.create('intersection', [c1, l2, 0]);
    
    var l3 = board.create('line', [i1, o1], { visible: false });
    var l4 = board.create('line', [o1, i2], { visible: false });
    
    // The tangents to circle c1 at points i3 and i4 are the
    // also tangent to circle c2
    var t1 = board.create('tangent', [c1, i3], { strokeColor: 'darkblue' });
    var t2 = board.create('tangent', [c1, i4], { strokeColor: 'darkblue' });
    
    // Supplements:
    // The arrows are just for illustration
    var v1 = board.create('arrow', [o1, i3], { strokeColor: 'lightblue', strokeWidth: 3 });
    var v2 = board.create('arrow', [o1, i4], { strokeColor: 'lightblue', strokeWidth: 3 });
    
    // t3 and t4 are the tangents to circle c4 through point o2
    var t3 = board.create('line', [o2, i1], { strokeColor: 'pink' });
    var t4 = board.create('line', [o2, i2], { strokeColor: 'pink' });
 </script> 

<jsxgraph width="100%" aspect-ratio="1 / 1" title="Tangent lines simultaneously to 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 ShareAlike 4.0 International License.
   https://creativecommons.org/licenses/by-sa/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: [-8, 8, 8, -8],
       keepaspectratio: true
   });
   
   // Define the two circles
   var o1 = board.create('point', [-2, 2], { name: 'O_1' });
   var o2 = board.create('point', [3, -3], { name: 'O_2' });
   
   var p1 = board.create('point', [-3, 5], { name: 'P_1' });
   var p2 = board.create('point', [2, -3], { name: 'P_2' });
   
   var c1 = board.create('circle', [o1, p1]);
   var c2 = board.create('circle', [o2, p2]);
   
   // The construction of the tangents starts here:
   var m = board.create('midpoint', [o1, o2], { name: 'M' });
   var lm = board.create('line', [o1, o2], { strokeWidth: 1, strokeColor: 'gray' });
   
   // The circle with center M containing the two centers O_1 and O_2
   var c3 = board.create('circle', [m, o2], { strokeColor: 'green', strokeWidth: 1 });
   
   var c4 = board.create('circle', [o1, () => Math.abs(c1.Radius() - c2.Radius())], {
       strokeColor: 'purple',
       strokeWidth: 1
   });
   
   var i1 = board.create('intersection', [c3, c4, 0], { visible: true });
   var i2 = board.create('intersection', [c3, c4, 1], { visible: true });
   
   var l1 = board.create('line', [o1, i1], { visible: false });
   var l2 = board.create('line', [o1, i2], { visible: false });
   
   var i3 = board.create('intersection', [c1, l1, 0]);
   var i4 = board.create('intersection', [c1, l2, 0]);
   
   var l3 = board.create('line', [i1, o1], { visible: false });
   var l4 = board.create('line', [o1, i2], { visible: false });
   
   // The tangents to circle c1 at points i3 and i4 are the
   // also tangent to circle c2
   var t1 = board.create('tangent', [c1, i3], { strokeColor: 'darkblue' });
   var t2 = board.create('tangent', [c1, i4], { strokeColor: 'darkblue' });
   
   // Supplements:
   // The arrows are just for illustration
   var v1 = board.create('arrow', [o1, i3], { strokeColor: 'lightblue', strokeWidth: 3 });
   var v2 = board.create('arrow', [o1, i4], { strokeColor: 'lightblue', strokeWidth: 3 });
   
   // t3 and t4 are the tangents to circle c4 through point o2
   var t3 = board.create('line', [o2, i1], { strokeColor: 'pink' });
   var t4 = board.create('line', [o2, i2], { strokeColor: 'pink' });
</jsxgraph>