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Five Circle Theorem
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<iframe
src="https://jsxgraph.uni-bayreuth.de/share/iframe/five-circle-theorem"
style="border: 1px solid black; overflow: hidden; width: 550px; aspect-ratio: 55 / 65;"
name="JSXGraph example: Five Circle 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';
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;
// Blue points
var attr = {
name: '',
color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);
for (k = 0; k < 5; k++) {
l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}
// Intersection points: yellow
for (k = 0; k < 5; k++) {
i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}
for (k = 0; k < 5; k++) {
c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
strokeColor: 'gray', strokeWidth: 1,
point: {
visible: false
}
});
}
// Intersection points: red
for (k = 0; k < 5; k++) {
j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}
// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
strokeColor: 'red',
strokeWidth: 2,
point: {
strokeColor: '#000000',
fillColor: '#000000',
size: 1
}
});
</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: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;
// Blue points
var attr = {
name: '',
color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);
for (k = 0; k < 5; k++) {
l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}
// Intersection points: yellow
for (k = 0; k < 5; k++) {
i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}
for (k = 0; k < 5; k++) {
c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
strokeColor: 'gray', strokeWidth: 1,
point: {
visible: false
}
});
}
// Intersection points: red
for (k = 0; k < 5; k++) {
j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}
// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
strokeColor: 'red',
strokeWidth: 2,
point: {
strokeColor: '#000000',
fillColor: '#000000',
size: 1
}
});
<jsxgraph width="100%" aspect-ratio="1 / 1" title="Five Circle 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.
*/
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;
// Blue points
var attr = {
name: '',
color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);
for (k = 0; k < 5; k++) {
l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}
// Intersection points: yellow
for (k = 0; k < 5; k++) {
i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}
for (k = 0; k < 5; k++) {
c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
strokeColor: 'gray', strokeWidth: 1,
point: {
visible: false
}
});
}
// Intersection points: red
for (k = 0; k < 5; k++) {
j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}
// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
strokeColor: 'red',
strokeWidth: 2,
point: {
strokeColor: '#000000',
fillColor: '#000000',
size: 1
}
});
</jsxgraph>

Five Circle Theorem

Euclidean
Geometry
Web references
  • Wikipedia on five circle theorems
JSXGraph v1.11.1 Copyright (C) see https://jsxgraph.org
0,0
–o+←↓↑→
// Define the id of your board in BOARDID
const board = JXG.JSXGraph.initBoard(BOARDID, {
boundingbox: [-5, 5, 5, -5]
});
var p = [], l = [], i = [], c = [], j = [], k, cc;
// Blue points
var attr = {
name: '',
color: '#7355ff'
};
p[0] = board.create('point', [-2.5, -3], attr);
p[1] = board.create('point', [-0, 4], attr);
p[2] = board.create('point', [2.5, -3], attr);
p[3] = board.create('point', [-4, 0], attr);
p[4] = board.create('point', [4, 0], attr);
for (k = 0; k < 5; k++) {
l[k] = board.create('segment', [p[k], p[(k + 1) % 5]], {strokeColor: 'black', strokeWidth: 1});
}
// Intersection points: yellow
for (k = 0; k < 5; k++) {
i[k] = board.create('intersection', [l[k], l[(k + 2) % 5], 0], {name: '', color: '#EAEA00'});
}
for (k = 0; k < 5; k++) {
c[k] = board.create('circumcircle', [p[k], i[k], i[(k + 2) % 5]], {
strokeColor: 'gray', strokeWidth: 1,
point: {
visible: false
}
});
}
// Intersection points: red
for (k = 0; k < 5; k++) {
j[k] = board.create('intersection', [c[k], c[(k + 2) % 5], 0], {name: '', color: '#EA0000'});
}
// 6th circle: circumcircle
cc = board.create('circumcircle', [j[0], j[2], j[3]], {
strokeColor: 'red',
strokeWidth: 2,
point: {
strokeColor: '#000000',
fillColor: '#000000',
size: 1
}
});

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.