Derivation of Golden Ratio By trapezoid

						var board = JXG.JSXGraph.initBoard('box1', {
boundingbox: [-10, 10, 10, -10],showNavigation:false, showcopyright: false, axis: false,
});
var p1 = board.create('point', [6, 2.0],{face:'',fixed:true});
var p2 = board.create('point', [3.147, -6.76],{face:'',fixed:true,label:{offset:[-15,10]}});
var l1 = board.create('segment', [p1, p2],{dash:2});
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:' ',face:'',fixed:true});
// var l7 = board.create('segment', [p2, i4],{color:"red"});
var p4 = board.create('point', [p1.X()-l1.L(), p1.Y()],{face:'',fixed:true}); 
var p5 = board.create('point', [p2.X()-l1.L(), p2.Y()],{face:'',fixed:true});  
//var t1 = board.create('text',[-5,6,"C: "+i3.Y()]);
//var t2 = board.create('text',[-5,5,"B: "+p2.Y()]);
var l8 = board.create('segment', [p1, p4],);
var l9 = board.create('segment', [p2, p5],);
var l10 = board.create('segment', [p4, p5],);
var a1 = board.create('angle', [p1, i3, p2],{name:'72°',radius:1.5,label:{offset:[-10,-2]}});
 
					

The image appears in the following posts

Triangle posted 1 year ago

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