Goden ratio triangle for determination value of sin 18degree

						var board = JXG.JSXGraph.initBoard('box1', {
boundingbox: [-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: false,
var p1 = board.create('point', [4.23, 7.0],{face:'',fixed:true});
var p2 = board.create('point', [0, -6.0],{face:'',fixed:true,label:{offset:[-15,10]}});
var l1 = board.create('segment', [p1, p2]);
var perp1 = board.create('perpendicularsegment', [l1, p1],{visible:false});
//var g1 = board.create('glider', [-3.0, 1.5, perp1],);
var k  = 1/l1.getSlope();
var ang = Math.atan(k)
var xc = p1.X()-l1.L()*Math.cos(ang)/2;
var yc= p1.Y()+ l1.L()*Math.sin(ang/2);

//var t1 = board.create('text',[-3,9,'xc = '+xc.toFixed(0)]);
//var t2 = board.create('text',[-3,8,'yc = '+yc.toFixed(0)]);

var p3 = board.create('point', [xc, yc],{visible:false});

var l2 = board.create('segment', [p2, p3],{visible:false});
var l3 = board.create('segment', [p3, p1],{visible:false});
var c1 = board.create('circle', [p3, l3.L()],{visible:false});
 var i1 = board.create('intersection', [c1, l2, 1],{visible:false});
 var l4 = board.create('segment', [i1, p2],{visible:false});
 var c2 = board.create('circle', [p1, l1.L()],{visible:false});
 var c3 = board.create('circle', [p2, l4.L()],{visible:false});
 var i2 = board.create('intersection', [c2, c3, 0],{visible:false});
 var i3 = board.create('intersection', [c2, c3, 1],{name:'C',face:'',fixed:true});
 var l5 = board.create('segment', [p1, i3],);
 var l6 = board.create('segment', [p2, i3],);
 var i4 = board.create('intersection', [c3, l5, 1],{name:'D',face:'',fixed:true});
var l7 = board.create('segment', [p2, i4],);

var a1 = board.create('angle', [p2, p1, i3],{name:'36°',radius:2,label:{offset:[-8,0]}});
var pp2 = board.create('perpendicularpoint', [p1, l6],{face:''});
var l9 = board.create('segment', [p1, pp2],{dash:2});


The image appears in the following posts

Triangle posted 11 months ago

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