document.write( "Question 1087690: In triangle ABC, AB = 9, BC = 12, AC = 15, and CD is the angle bisector. Find the length of CD. \n" ); document.write( "

Algebra.Com's Answer #701999 by ikleyn(52803) $\"\"$ $\"About$

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document.write( "The key for solving this problem is this Theorem:\r\n" );
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document.write( "    In a triangle, the angle bisector divides the side to which it is drawn, in two segments \r\n" );
document.write( "    proportional to the ratio of two other sides of a triangle.\r\n" );
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document.write( "(see the lesson On what segments the angle bisector divides the side of a triangle in this site).\r\n" );
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document.write( "For our triangle ABC it means that  =  =  = .\r\n" );
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document.write( "OK. Then, together with BD + AD = AB = 9 it means that BD = 4 and AD = 5.\r\n" );
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document.write( "Next, I am sure that you understand, without my explanations, that the triangle ABC is right-angled, since AC =  = 15 ).\r\n" );
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document.write( "Finally, CD =  =  =  =  = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( " GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Properties of triangles\".\r
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