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Tangents on circle
This JSXGraph demo shows the __polar of a point__ with respect to a circle. If point *p* lies outside circle *c*, the polar line is constructed with the two tangents from $p$ to the circle. The intersections of the tangents with the circle define two points which define the *polar line*. If $p$ is on the circle, the polar line is tangent to the circle through $p$.
If you look at the code, the construction is the other way round:
```
t = board.create('tangent', [c, p]);
```
constructs the polar line of $p$. The intersection points of the polar line $t$ with the circle are those points which define the tangent line through the point $p$, i.e. where the circle is touched by the tangents to the circle through $p$.
// Define the id of your board in BOARDID
var board = JXG.JSXGraph.initBoard(BOARDID, { boundingbox: [-5, 5, 5, -5], keepaspectratio: true });
// Set some point attributes.
board.options.point.strokeColor = 'red';
board.options.point.fillColor = 'red';
board.options.point.strokeOpacity = 0.8;
board.options.point.fillOpacity = 0.8;
var m = board.create('point', [0.5, 0.3]);
var b = board.create('point', [3, 0]);
var c = board.create('circle', [m, b]);
var p = board.create('point', [-4, 2], {name: 'p', label: {autoPosition: true}});
// If p is not on c, the tangent is the polar.
var t = board.create('tangent', [c, p], { name: 'polar', withLabel: true, label: {position: '0.7 left', distance: 0.5} });
var i1 = board.create('intersection', [c, t, 0], { visible: false });
var i2 = board.create('intersection', [c, t, 1], { visible: false });
var t1 = board.create('tangent', [c, i1]);
var t2 = board.create('tangent', [c, i2]);
This example is licensed under a
Creative Commons Attribution ShareAlike 4.0 International License.
Please note you have to mention
The Center of Mobile Learning with Digital Technology
in the credits.