document.write( "Question 86741: find the radius of the circle inscribed in the triangle bounded by the lines x-y+4=0, 7x-y-2=0 and x+y+4=0.\r
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Algebra.Com's Answer #62779 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
find the radius of the circle inscribed in the triangle bounded by the lines x-y+4=0, 7x-y-2=0 and x+y+4=0.
\n" ); document.write( "actually i graph the equation and prove that x-y+4 is perpendicular to the line x+y+4. got all the points of the triangle (1,5), (-4,0) and (-1/4, -3.75), got stuck with the circle thing.. could you help me please?
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document.write( "That's not quite the way to do the problem:\r\n" );
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document.write( "The formula is\r\n" );
document.write( "                                           TRIANGLE'S AREA\r\n" );
document.write( "RADIUS OF INSCRIBED CIRCLE OF TRIANGLE = --------------------\r\n" );
document.write( "                                          HALF ITS PERIMETER\r\n" );
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document.write( "We first find the three corners of the triangle:\r\n" );
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document.write( " x - y + 4 = 0\r\n" );
document.write( "7x - y - 2 = 0\r\n" );
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document.write( "Solve that pair and get one corner point (1,5) \r\n" );
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document.write( " x - y + 4 = 0\r\n" );
document.write( " x + y + 4 = 0\r\n" );
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document.write( "Solve that pair and get the second corner point (-4,0)\r\n" );
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document.write( "7x - y - 2 = 0\r\n" );
document.write( " x + y + 4 = 0\r\n" );
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document.write( "Solve that pair and get the second corner point (\"-1%2F4\",\"-15%2F4\")\r\n" );
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document.write( "Now we find its area, using the determinant formula:\r\n" );
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document.write( "`                         |x1 y1 1|\r\n" );
document.write( "A = absolute value of:  \"1%2F2\"|x2 y2 1|\r\n" );
document.write( "`                         |x3 y3 1|\r\n" );
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document.write( "`                         |  1   5  1|\r\n" );
document.write( "A = absolute value of:  \"1%2F2\"| -4   0  1|\r\n" );
document.write( "`                         |\"-1%2F4\"\"-15%2F4\" 1|\r\n" );
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document.write( "A = absolute value of \"1%2F2\"\"%2875%2F2%29\" = \"75%2F4\"\r\n" );
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document.write( "TRIANGLE's AREA = \"75%2F4\"\r\n" );
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document.write( "Now we have to find the perimeter.\r\n" );
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document.write( "The side of the triangle between (1,5) and (-4,0) is\r\n" );
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document.write( "D = \"sqrt%28%28-4-1%29%5E2%2B%280-5%29%5E2%29\"} = \"sqrt%28%28-5%29%5E2+%2B+%28-5%29%5E2%29\" = \"sqrt%2825%2B25%29\" = \"sqrt%2850%29\" = \"sqrt%2825%2A2%29\" = \"5sqrt%282%29\"\r\n" );
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document.write( "The side of the triangle between (1,5) and (-1/4,-15/4) is\r\n" );
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document.write( "D = \"sqrt%28%28-1%2F4-1%29%5E2%2B%28-15%2F4-5%29%5E2%29\"} = \"sqrt%28%28-1%2F4-4%2F4%29%5E2+%2B+%28-15%2F4-20%2F4%29%5E2%29\" = \"sqrt%28%28-5%2F4%29%5E2%2B%28-35%2F4%29%5E2%29\" =\r\n" );
document.write( "\"sqrt%2825%2F16%2B1225%2F16%29\" = \"sqrt%281250%2F16%29\" = \"sqrt%281250%29%2F4\" = \"sqrt%28625%2A2%29%2F4\" = \"25sqrt%282%29%2F4\"\r\n" );
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document.write( "The side of the triangle between (-4,0) and (-1/4,-15/4) is\r\n" );
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document.write( "D = \"sqrt%28%28-1%2F4-%28-4%29%29%5E2%2B%28-15%2F4-0%29%5E2%29\"} = \"sqrt%28%28-1%2F4%2B4%29%5E2+%2B+%28-15%2F4%29%5E2%29\" = \"sqrt%28%28-1%2F4%2B16%2F4%29%5E2%2B%28-15%2F4%29%5E2%29\" =\r\n" );
document.write( "\"sqrt%28%2815%2F4%29%5E2%2B225%2F16%29\" = \"sqrt%28225%2F16+%2B+225%2F16%29\" = \"sqrt%28450%2F16%29\" = \"sqrt%28450%29%2F4\" = \"sqrt%28225%2A2%29%2F4\" = \"15sqrt%282%29%2F4\"\r\n" );
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document.write( "So the perimeter is\r\n" );
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document.write( "\"5sqrt%282%29\" + \"25sqrt%282%29%2F4\" + \"15sqrt%282%29%2F4\" =\r\n" );
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document.write( "\"20sqrt%282%29%2F4\" + \"25sqrt%282%29%2F4\" + \"15sqrt%282%29%2F4\" =\r\n" );
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document.write( "\"60sqrt%282%29%2F4\" = \"15sqrt%282%29\"\r\n" );
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document.write( "One-half the perimeter (semiperimeter) = \"15sqrt%282%29%2F2\"\r\n" );
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document.write( "Now we can use the formula:\r\n" );
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document.write( "                                           TRIANGLE'S AREA\r\n" );
document.write( "RADIUS OF INSCRIBED CIRCLE OF TRIANGLE = --------------------\r\n" );
document.write( "                                          HALF ITS PERIMETER\r\n" );
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document.write( "RADIUS OF INSCRIBED CIRCLE OF TRIANGLE =\"%2875%2F4%29%2F%2815sqrt%282%29%2F2%29\" \r\n" );
document.write( "                                          \r\n" );
document.write( "RADIUS OF INSCRIBED CIRCLE OF TRIANGLE =\"%2875%2F4%29%282%2F15sqrt%282%29%29\" = \"5%2F%282sqrt%282%29%29\" = \"%285sqrt%282%29%29%2F%282sqrt%282%29sqrt%282%29%29\"\r\n" );
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document.write( "RADIUS OF INSCRIBED CIRCLE OF TRIANGLE =\"5sqrt%282%29%2F4\"\r\n" );
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document.write( "Here's the graph:\r\n" );
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document.write( "Edwin
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