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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\n" ); document.write( "\n" ); document.write( "The sides of triangle ABC are 3, 5, and 7. \n" ); document.write( "

Algebra.Com's Answer #851605 by EPM(3) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "I admit I have never heard of Ikleyn's theorem:\r\n" );
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document.write( "If two triangles have a common altitude, then the ratio of their areas\r\n" );
document.write( "equals the ratio of the bases of these triangles.  \r\n" );
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document.write( "I cannot even find it anywhere online.\r\n" );
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document.write( "The common altitude for the two triangles was not even drawn. It is on the\r\n" );
document.write( "extension of CA, located outside triangle ABC.\r\n" );
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document.write( "Here, I have drawn in the common altitude BE.  But this is far from \r\n" );
document.write( "obvious, especially since the common altitude was not even drawn.\r\n" );
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document.write( "I agree that this is true:\r\n" );
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document.write( "but I am amazed that it occurred to you.  It certainly would not\r\n" );
document.write( "have occurred to any ordinary student.  My hat is off to you for \r\n" );
document.write( "coming up with that theorem.  Is it included in any geometry book?\r\n" );
document.write( "As I said above, I cannot find it online.\r\n" );
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document.write( "Thank you for introducing me to Ikleyn's theorem.  My only complaint\r\n" );
document.write( "is that you assumed that it was something any student would \r\n" );
document.write( "immediately recognize, without mentioning anything about the\r\n" );
document.write( "two triangles having a common altitude.\r\n" );
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document.write( "EDIT LATER:\r\n" );
document.write( "I finally found Ikleyn's theorem online.  It's called the \r\n" );
document.write( "\"Same Altitude Principle\" on this site:\r\n" );
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document.write( "https://www.youtube.com/watch?v=MQSClqinLUw\r\n" );
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document.write( "Edwin

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