document.write( "Question 1210173: Let P be a point chosen uniformly at random inside triangle ABC. Extend ray BP to hit side AC at D. What is the probability that BD < 4?\r
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Algebra.Com's Answer #851597 by AnlytcPhil(1806) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Ikleyn's solution is incorrect.  But she refuses to admit her error.  \r\n" );
document.write( "She apparently thinks there is a theorem that states:\r\n" );
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document.write( "There is no such theorem but Ikleyn believed she could\r\n" );
document.write( "use it anyway to show that\r\n" );
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document.write( "Below is the correct solution.  It's very long, which is why I did not have\r\n" );
document.write( "time to finish the other day, and thought someone else might take over.  I\r\n" );
document.write( "have checked it thoroughly and have found no errors. \r\n" );
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document.write( "Ikleyn made a bad assumption, but when I challenged her, she wanted to fight,\r\n" );
document.write( "and accused me of being the one wanting to fight.\r\n" );
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document.write( "We use the law of cosines to find angle A:\r\n" );
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document.write( "We find the area of triangle ABC\r\n" );
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document.write( "We use the law of cosines on triangle ABD' to find AD':\r\n" );
document.write( "(note: We could use the law of sines, but the law of cosines\r\n" );
document.write( "will give us AD' more directly)\r\n" );
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document.write( ", ignore the minus sign:\r\n" );
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document.write( "We find the area of triangle ABD'\r\n" );
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document.write( "The desired probability is the ratio of the area of triangle ABD' to\r\n" );
document.write( "the area of triangle ABC.\r\n" );
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document.write( "Multiply top and bottom by 8\r\n" );
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document.write( "  <-- correct answer, the probability that BD < 4.\r\n" );
document.write( "That is approximately 0.308276253\r\n" );
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document.write( "Edwin

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