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| Line 1: |
Line 1: |
| − | [center][b]bjc's Entry:[/b][/center]
| + | Hi |
| − | 3-4-5 triangle with circumcircle/center, incircle/center, orthocenter, centroid and 3 excircles
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| − | [asy]
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| − | size(12cm);
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| − | dot((0,0));
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| − | dot((4,0));
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| − | dot((0,3));
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| − | dot((2,1.5));
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| − | dot((1,1));
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| − | dot((1.333,1));
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| − | dot((6,6));
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| − | dot((-2,2));
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| − | dot((3,-3));
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| − | draw((0,0)--(4,0)--(0,3)--(0,0));
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| − | draw((0,3)--(2,0));
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| − | draw((4,0)--(0,1.5));
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| − | draw(circle((2,1.5) , 2.5));
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| − | draw(circle((1,1) , 1));
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| − | draw(circle((6,6) , 6));
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| − | draw(circle((-2,2) , 2));
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| − | draw(circle((3,-3) , 3));
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| − | draw((-2,4.5)--(8,-3));
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| − | draw((0,0)--(2,1.5));
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| − | draw((0,-4.5)--(0,6.5));
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| − | draw((-2.5,0)--(6.5,0));
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| − | label( "<math>A=H</math>" , (0,0), SW);
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| − | label( "<math>B</math>" , (4,0), E);
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| − | label( "<math>C</math>" , (0,3), N);
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| − | label( "<math>G</math>" , (1.33333,1) , S);
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| − | label( "<math>O</math>" , (2,1.5), NE);
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| − | label( "<math>3</math>" , (0,0)--(0,3) , W);
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| − | label( "<math>4</math>" , (0,0)--(4,0) , S);
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| − | label( "<math>5</math>" , (0,4.6)--(3.9,0));
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| − | label( "<math>I</math>" , (1,1) , W);
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| − | label( "<math>O_A</math>" , (6,6) , SW);
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| − | label( "<math>O_B</math>" , (-2,2) , SW);
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| − | label( "<math>O_C</math>" , (3,-3) , S);
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| − | [/asy]
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