document.write( "Question 1208063: The area of △ABC is 40. Points P, Q and R lie on sides AB, BC and CA respectively. If AP = 3 and PB = 5, and the area of △ABQ is equal to the area of PBQR, determine the area of △AQC? \n" ); document.write( "
Algebra.Com's Answer #846243 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "There is a fallacy in Ikleyn's proof above.  I will draw just enough of it to\r\n" );
document.write( "show the fallacy.  While she is correct that triangles AOP and QOR are\r\n" );
document.write( "congruent, QR is not necessarily parallel to AP, and therefore not necessarily\r\n" );
document.write( "parallel to AB as she has stated. I do not see that she has proved it parallel.\r\n" );
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document.write( "We must rule out the possibility of the figure on the right below, and show that\r\n" );
document.write( "the figure on the left is the correct one. She is correct that QR = AP = 3, but\r\n" );
document.write( "she must show that QR is parallel to AP.  I think she can show this by making\r\n" );
document.write( "use of the fact that QR = 3 and the converse of this well-known theorem:\r\n" );
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document.write( "If a line parallel to one side of a triangle intersects the other two sides, \r\n" );
document.write( "then it divides the two sides proportionally. (The converse is also true.)\r\n" );
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document.write( "If Ikleyn will correct this error in her proof, I will delete this post. So that\r\n" );
document.write( "the student will learn of the corrected proof, I will make another post in\r\n" );
document.write( "one of my other screen names, to inform him or her of the correction.  \r\n" );
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document.write( "Below I have drawn the figure for the whole problem, but I purposely drew QR to\r\n" );
document.write( "look not quite parallel to AB, which Ikleyn will prove it to be. She is welcome\r\n" );
document.write( "to use my figure below.  \r\n" );
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document.write( "Edwin
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