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tutorbot2.html
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<!DOCTYPE html>
<html>
<head>
<title>tutorbot</title>
<link rel="stylesheet" href="tutorbot.css" media="screen">
<link rel="stylesheet" type="text/css" href="jsxgraph.css" />
<link rel="stylesheet" type="text/css" href="tutorbot.css" />
<script type="text/javascript" src="jsxgraphcore.js"></script>
</head>
<body>
<div id="box" style="float:left;width:400px; height:400px;">
</div>
<div id = "solutionbox" style= "width:50%;float:left;margin-left:7%">
<div class = "pullleft width7">
Given:
</div>
<div class = "pullleft">
ABCD is a parallelogram
</div>
<hr style = "clear:both;"/>
<div class = "pullleft width7">
To Prove:
</div>
<div class = "pullleft">
ABCD is a rhombus
</div>
<hr style = "clear:both;"/>
<div class = "pullleft width7">
Proof:
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AP = AS = x<br/>
SD = DR = y<br/>
PB = BQ = a<br/>
CR = CQ = b<br/>
</div>
<div class = "reasondiv">
External Tangents from a point to circle are equal.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB = AP + PB = x + a
<br/>
AD = AS + SD = x + y
<br/>
BC = BQ + QC = a + b
<br/>
CD = CR + RD = y + b
</div>
<div class = "reasondiv">
Points A,P,B are collinear.<br/>
Points A,S,D are collinear.<br/>
Points B,Q,C are collinear.<br/>
Points C,R,D are collinear.<br/>
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB + CD = x+a+y+b<br/>
AD + BC = x+a+y+b<br/>
∴ AB + CD = AD + BC, <br/>
</div>
<div class = "reasondiv">
From previous point, adding two sides.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB = CD , AD = BC<br/>
2AB = 2AD and also: <br/>
2CD = 2BC<br/>
AB = AD and CD = BC
</div>
<div class = "reasondiv">
<br/>
opposite sides of parallelogram are equal.
</div>
<hr style = "clear:both;"/>
<div class = "statementdiv">
AB = AD = CD = BC <br/>
and hence<br/>
ABCD is a rhombus.
</div>
<div class = "reasondiv">
opposite and adjacent sides of quadrilateral ABCD are equal.
</div>
<hr style = "clear:both;"/>
<br/><br/>
</div>
<!-- solutionbox ends above -->
<script type="text/javascript">
var board = JXG.JSXGraph.initBoard('box',{axis:false, showNavigation:false, showCopyright:false});
var center = board.create('point', [0.0, 0.0],{name:'O'});
var circle = board.create('circle', [center, 3]);
var r = board.create('glider', [0.0,-3.0,circle],{name:'R'});
var q = board.create('glider', [3.0,0.0,circle],{name:'Q'});
var p = board.create('glider', [0.0,3.0,circle],{name:'P'});
var s = board.create('glider', [-3.0,0.0,circle],{name:'S'});
var t1 = board.create('tangent', [p]);
var t2 = board.create('tangent', [q]);
var t3 = board.create('tangent', [r]);
var t4 = board.create('tangent', [s]);
var a = board.create('point', [-3.0, 3.0],{name:'A'});
var b = board.create('point', [3.0, 3.0],{name:'B'});
var c = board.create('point', [3.0, -3.0],{name:'C'});
var d = board.create('point', [-3.0,-3.0],{name:'D'});
var l1 = board.create('segment', [p, r]);
var l2 = board.create('segment', [b, d]);
</script>
</body>
</html>