document.write( "Question 388780: an isosceles triangle, whose legs are each 13, is inscribed in a circle. if the altitude to the base of the triangle is 5, find the radius of the circle. \n" ); document.write( "
Algebra.Com's Answer #275205 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's solution is incorrect.\r\n" );
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document.write( "Draw in the radii to the vertices:\r\n" );
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document.write( "Extend the vertical radius down to the base of the given triangle,\r\n" );
document.write( "which we label D, and we let x be the measure of OD\r\n" );
document.write( "dividing the base into two equal parts, each measuring 2.5:\r\n" );
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document.write( "From right triangle BOD  \r\n" );
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document.write( "\"BD%5E2%2BDO%5E2=BO%5E2\"\r\n" );
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document.write( "\"r%5E2=2.5%5E2%2Bx%5E2\"\r\n" );
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document.write( "\"r%5E2=6.25%2Bx%5E2\"\r\n" );
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document.write( "\"r%5E2-x%5E2=6.25\"\r\n" );
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document.write( "\"%28r-x%29%28r%2Bx%29=6.25\"\r\n" );
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document.write( "From right triangle BAD\r\n" );
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document.write( "\"%28r%2Bx%29%5E2+%2B+2.5%5E2+=+13%5E2\"\r\n" );
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document.write( "\"%28r%2Bx%29%5E2+%2B+6.25+=+169\"\r\n" );
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document.write( "\"%28r%2Bx%29%5E2+%2B+6.25+=+169\"\r\n" );
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document.write( "\"%28r%2Bx%29%5E2+=+162.75\"\r\n" );
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document.write( "\"r%2Bx+=+%22%22+%2B-+sqrt%28162.75%29\"\r\n" );
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document.write( "Ignore the negative:\r\n" );
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document.write( "\"r%2Bx+=++sqrt%28162.75%29\"\r\n" );
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document.write( "\"r%2Bx+=++sqrt%28162.75%29\"\r\n" );
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document.write( "\"r%2Bx+=+12.75735082\"\r\n" );
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document.write( "Substitute \"sqrt%28162.75%29\" for \"r%2Bx%29\" in\r\n" );
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document.write( "\"%28r-x%29%28r%2Bx%29=6.25\"\r\n" );
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document.write( "\"%28r-x%29sqrt%28162.75%29=6.25\"\r\n" );
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document.write( "\"r-x=6.25%2Fsqrt%28162.75%29\"\r\n" );
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document.write( "\"r-x=0.489913626\"\r\n" );
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document.write( "Add these two equations:\r\n" );
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document.write( "\"system%7Br%2Bx+=+12.75735082%2C+r-x=0.489913626\"\r\n" );
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document.write( "2r = 13.24728445\r\n" );
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document.write( " r = 6.62363632224\r\n" );
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document.write( "Edwin
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