Circum circles of subtriangles - Revision history

A WASSERMANN at 09:56, 18 January 2021

2021-01-18T09:56:37Z

← Older revision	Revision as of 09:56, 18 January 2021
(No difference)

Michael at 12:52, 7 June 2011

2011-06-07T12:52:47Z

← Older revision		Revision as of 12:52, 7 June 2011
Line 50:		Line 50:
	p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});		p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});

	b1 = brd.create('~~line~~',['A','B'],{name:''~~,straightFirst:false,straightLast:false~~});		b1 = brd.create('segment',['A','B'],{name:''});
	b2 = brd.create('~~line~~',['A','C'],{name:''~~,straightFirst:false,straightLast:false~~});		b2 = brd.create('segment',['A','C'],{name:''});
	b3 = brd.create('~~line~~',['C','B'],{name:''~~,straightFirst:false,straightLast:false~~});		b3 = brd.create('segment',['C','B'],{name:''});

	c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});		c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});

Michael at 12:52, 7 June 2011

2011-06-07T12:52:29Z

← Older revision		Revision as of 12:52, 7 June 2011
Line 11:		Line 11:
	p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});		p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});

	b1 = brd.create('~~line~~',['A','B'],{name:''~~,straightFirst:false,straightLast:false~~});		b1 = brd.create('segment',['A','B'],{name:''});
	b2 = brd.create('~~line~~',['A','C'],{name:''~~,straightFirst:false,straightLast:false~~});		b2 = brd.create('segment',['A','C'],{name:''});
	b3 = brd.create('~~line~~',['C','B'],{name:''~~,straightFirst:false,straightLast:false~~});		b3 = brd.create('segment',['C','B'],{name:''});

	c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});		c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});

Michael at 12:51, 7 June 2011

2011-06-07T12:51:47Z

← Older revision		Revision as of 12:51, 7 June 2011
Line 7:		Line 7:
	<jsxgraph width="800" height="600">		<jsxgraph width="800" height="600">
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
	~~brd.suspendUpdate();~~
	p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});
Line 16:		Line 15:
	b3 = brd.create('line',['C','B'],{name:'',straightFirst:false,straightLast:false});		b3 = brd.create('line',['C','B'],{name:'',straightFirst:false,straightLast:false});

	c1 = brd.create('circumcircle',['A','B','C'],{name:''});		c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});
	c1~~[1]~~.setProperty('strokeColor:#AAAAAA');		c1.setProperty('strokeColor:#AAAAAA');
	~~c1[0].hideElement(); // hide center of circle~~

	l1 = brd.create('bisector',['B','A','C'],{name:'',visible:false}); // alpha		l1 = brd.create('bisector',['B','A','C'],{name:'',visible:false}); // alpha
Line 28:		Line 26:
	pp3 = brd.create('perpendicularpoint',[i1,b3],{name:"A'",fillColor:'blue'});		pp3 = brd.create('perpendicularpoint',[i1,b3],{name:"A'",fillColor:'blue'});

	c2 = brd.create('circumcircle',[pp1,pp2,pp3],{name:''});		c2 = brd.create('circumcircle',[pp1,pp2,pp3],{name:'', strokeColor: '#3CB371', point: {visible: false}});
	c2[1].~~setProperty~~('strokeColor:#~~3CB371~~');		c3 = brd.create('circumcircle',[p3,pp2,pp3],{name:'', strokeColor: '#FF8C00', point: {visible: false}});
	c2[0]~~.hideElement(~~);		c4 = brd.create('circumcircle',[p2,pp1,pp3],{name:'', strokeColor: '#FF8C00', point: {visible: false}});
			c5 = brd.create('circumcircle',[p1,pp2,pp1],{name:'', strokeColor: '#FF8C00', point: {visible: false}});

	c3 = brd.create('~~circumcircle~~',[p3,~~pp2~~,~~pp3~~],{name:''});		i2 = brd.create('otherintersection',[c3,c1,p3],{name:"C''",fillColor:'blue'});
	c3[1]~~.setProperty(~~'~~strokeColor~~:~~#FF8C00~~');		i3 = brd.create('otherintersection',[c4,c1,p2],{name:"B''",fillColor:'blue'});
	c3[0]~~.hideElement(~~);		i4 = brd.create('otherintersection',[c5,c1,p1],{name:"A''",fillColor:'blue'});

	~~c4 = brd.create('circumcircle',[p2,pp1,pp3],{name:''});~~		ll1 = brd.create('segment',[i2,pp1],{name:'',strokeColor:'#FF6347'});
	~~c4[1].setProperty('strokeColor:#FF8C00');~~		ll2 = brd.create('segment',[i3,pp2],{name:'',strokeColor:'#FF6347'});
	~~c4[0].hideElement();~~		ll3 = brd.create('segment',[i4,pp3],{name:'',strokeColor:'#FF6347'});

	~~c5 = brd.create('circumcircle',[p1,pp2,pp1],{name:''});~~
	~~c5[1].setProperty('strokeColor:#FF8C00');~~
	~~c5[0].hideElement();~~

	~~i2 = brd.create('otherintersection',[c3[1],c1[1],p3],{name:"C''",fillColor:'blue'});~~
	~~i3 = brd.create('otherintersection',[c4[1],c1[1],p2],{name:"B''",fillColor:'blue'});~~
	~~i4 = brd.create('otherintersection',[c5[1],c1[1],p1],{name:"A''",fillColor:'blue'});~~

	ll1 = brd.create('~~line~~',[i2,pp1],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});
	ll2 = brd.create('~~line~~',[i3,pp2],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});
	ll3 = brd.create('~~line~~',[i4,pp3],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});

	i5 = brd.create('intersection',[ll1,ll2,0],{name:"P",fillColor:'#9932CC',strokeColor:'#9932CC'});		i5 = brd.create('intersection',[ll1,ll2,0],{name:"P",fillColor:'#9932CC',strokeColor:'#9932CC'});
	brd.~~unsuspendUpdate~~();		brd.update();
	</jsxgraph>		</jsxgraph>

Line 59:		Line 46:
	<source lang="javascript">		<source lang="javascript">
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
	~~brd.suspendUpdate();~~
	p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});
Line 68:		Line 54:
	b3 = brd.create('line',['C','B'],{name:'',straightFirst:false,straightLast:false});		b3 = brd.create('line',['C','B'],{name:'',straightFirst:false,straightLast:false});

	c1 = brd.create('circumcircle',['A','B','C'],{name:''});		c1 = brd.create('circumcircle',['A','B','C'],{name:'', point: {visible: false}});
	c1~~[1]~~.setProperty('strokeColor:#AAAAAA');		c1.setProperty('strokeColor:#AAAAAA');
	~~c1[0].hideElement(); // hide center of circle~~

	l1 = brd.create('bisector',['B','A','C'],{name:'',visible:false}); // alpha		l1 = brd.create('bisector',['B','A','C'],{name:'',visible:false}); // alpha
Line 80:		Line 65:
	pp3 = brd.create('perpendicularpoint',[i1,b3],{name:"A'",fillColor:'blue'});		pp3 = brd.create('perpendicularpoint',[i1,b3],{name:"A'",fillColor:'blue'});

	c2 = brd.create('circumcircle',[pp1,pp2,pp3],{name:''~~});~~		c2 = brd.create('circumcircle',[pp1,pp2,pp3],{name:'', strokeColor: '#3CB371', point: {visible: false}});
	~~c2[1].setProperty('~~strokeColor:#3CB371');		c3 = brd.create('circumcircle',[p3,pp2,pp3],{name:'', strokeColor: '#FF8C00', point: {visible: false}});
	~~c2[0].hideElement();~~		c4 = brd.create('circumcircle',[p2,pp1,pp3],{name:'', strokeColor: '#FF8C00', point: {visible: false}});
			c5 = brd.create('circumcircle',[p1,pp2,pp1],{name:'', strokeColor: '#FF8C00', point: {visible: false}});
	c3 = brd.create('circumcircle',[p3,pp2,pp3],{name:''~~});~~
	~~c3[1].setProperty('~~strokeColor:#FF8C00');
	~~c3[0].hideElement();~~

	c4 = brd.create('circumcircle',[p2,pp1,pp3],{name:''~~});~~
	~~c4[1].setProperty('~~strokeColor:#FF8C00');
	~~c4[0].hideElement();~~

	c5 = brd.create('circumcircle',[p1,pp2,pp1],{name:''~~});~~
	~~c5[1].setProperty('~~strokeColor:#FF8C00');
	~~c5[0].hideElement(~~);

	i2 = brd.create('otherintersection',[c3~~[1]~~,c1~~[1]~~,p3],{name:"C''",fillColor:'blue'});		i2 = brd.create('otherintersection',[c3,c1,p3],{name:"C''",fillColor:'blue'});
	i3 = brd.create('otherintersection',[c4~~[1]~~,c1~~[1]~~,p2],{name:"B''",fillColor:'blue'});		i3 = brd.create('otherintersection',[c4,c1,p2],{name:"B''",fillColor:'blue'});
	i4 = brd.create('otherintersection',[c5~~[1]~~,c1~~[1]~~,p1],{name:"A''",fillColor:'blue'});		i4 = brd.create('otherintersection',[c5,c1,p1],{name:"A''",fillColor:'blue'});

	ll1 = brd.create('~~line~~',[i2,pp1],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});		ll1 = brd.create('segment',[i2,pp1],{name:'',strokeColor:'#FF6347'});
	ll2 = brd.create('~~line~~',[i3,pp2],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});		ll2 = brd.create('segment',[i3,pp2],{name:'',strokeColor:'#FF6347'});
	ll3 = brd.create('~~line~~',[i4,pp3],{name:''~~,straightFirst:false,straightLast:false~~,strokeColor:'#FF6347'});		ll3 = brd.create('segment',[i4,pp3],{name:'',strokeColor:'#FF6347'});

	i5 = brd.create('intersection',[ll1,ll2,0],{name:"P",fillColor:'#9932CC',strokeColor:'#9932CC'});		i5 = brd.create('intersection',[ll1,ll2,0],{name:"P",fillColor:'#9932CC',strokeColor:'#9932CC'});
	brd.~~unsuspendUpdate~~();		brd.update();
	</source>		</source>

	[[Category:Examples]]		[[Category:Examples]]
	[[Category:Geometry]]		[[Category:Geometry]]

A WASSERMANN at 09:00, 8 September 2010

2010-09-08T09:00:22Z

← Older revision		Revision as of 09:00, 8 September 2010
Line 8:		Line 8:
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	p1 = brd.create'point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});
	p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});		p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});
Line 60:		Line 60:
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
	brd.suspendUpdate();		brd.suspendUpdate();
	p1 = brd.create'point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.create('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.create('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});
	p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});		p3 = brd.create('point', [2,3] , {name:'C',fillColor:'red',strokeColor:'red'});

A WASSERMANN at 08:59, 8 September 2010

2010-09-08T08:59:52Z

Show changes

A WASSERMANN at 11:20, 22 September 2009

2009-09-22T11:20:11Z

← Older revision		Revision as of 11:20, 22 September 2009
Line 1:		Line 1:
	Let ABC be a triangle and let the incircle intersect BC, CA, and AB at A', B', and C', respectively.		Let ABC be a triangle and let the incircle intersect <math>BC</math>, <math>CA</math>, and <math>AB</math> at <math>A'</math>, <math>B'</math>, and <math>C'</math>, respectively.

	Let the circumcircles of AB'C', A'BC', and A'B'C intersect the circumcircle of ABC (apart from A, B, and C) at A'', B'', and C'', respectively.		Let the circumcircles of <math>AB'C'</math>, <math>A'BC'</math>, and <math>A'B'C</math> intersect the circumcircle of <math>ABC</math> (apart from <math>A</math>, <math>B</math>, and <math>C</math>) at <math>A''</math>, <math>B''</math>, and <math>C''</math>, respectively.

	Then A'A'', B'B'', and C'C'' meet in one point, P.		Then <math>A'A''</math>, <math>B'B''</math>, and <math>C'C''</math> meet in one point, <math>P</math>.

	<jsxgraph width="800" height="600">		<jsxgraph width="800" height="600">

A WASSERMANN at 11:18, 22 September 2009

2009-09-22T11:18:03Z

@@ Line 1: / Line 1: @@
 <jsxgraph width="800" height="600">
 brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
@@ Line 46: / Line 52: @@
 i5 = brd.createElement('intersection',[ll1,ll2,0],{name:"P",fillColor:'#9932CC',strokeColor:'#9932CC'});
-</jsxgraph>
+c5 = brd.createElement('circumcircle',[p1,pp2,pp1],{name:''});
 [[Category:Examples]]
 [[Category:Geometry]]

A WASSERMANN at 11:16, 22 September 2009

2009-09-22T11:16:41Z

← Older revision		Revision as of 11:16, 22 September 2009
Line 1:		Line 1:
	<jsxgraph width="800" height="600">		<jsxgraph width="800" height="600">
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[0,4,12,-4], keepaspectratio:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-1,4,12,-4], keepaspectratio:true});
	p1 = brd.createElement('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.createElement('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.createElement('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.createElement('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});

A WASSERMANN at 11:16, 22 September 2009

2009-09-22T11:16:30Z

← Older revision		Revision as of 11:16, 22 September 2009
Line 1:		Line 1:
	<jsxgraph width="800" height="600">		<jsxgraph width="800" height="600">
	brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[-4,4,12,-4], keepaspectratio~~:true,axis~~:true});		brd = JXG.JSXGraph.initBoard('jxgbox', {boundingbox:[0,4,12,-4], keepaspectratio:true});
	p1 = brd.createElement('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});		p1 = brd.createElement('point', [0.5,-1.5] , {name:'A',fillColor:'red',strokeColor:'red'});
	p2 = brd.createElement('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});		p2 = brd.createElement('point', [7.5,0.5] , {name:'B',fillColor:'red',strokeColor:'red'});