document.write( "Question 737531: In the diagram below, ΔABC is circumscribed about circle O and the sides of ΔABC are tangent to the circle at points D, E, and F.
\n" ); document.write( "http://imageshack.us/photo/my-images/849/geou.png/
\n" ); document.write( "If AB=20, AE=12, and CF=15, what is the length of AC? \n" ); document.write( "

Algebra.Com's Answer #450427 by MathLover1(20849) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "If $\"AB=20\"$ ,
\n" ); document.write( " $\"AE=12\"$ , and
\n" ); document.write( " $\"CF=15\"$ ,
\n" ); document.write( "what is the length of $\"AC\"$ ? \r
\n" ); document.write( "\n" ); document.write( "Incenter :
\n" ); document.write( "The location of the center of the $\"incircle\"$ . The point where the $\"angle\"$ $\"bisectors\"$ meet. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "If $\"AB=20\"$ and $\"AE=12\"$ , then $\"EB=8\"$ \r
\n" ); document.write( "\n" ); document.write( "since $\"EO=FO=DO\"$ , angle $\"EBO\"$ = angle $\"FBO\"$ , and $\"BO=BO\"$ .....=> triangles $\"EOB\"$ and $\"OBF\"$ are $\"congruent\"$ , then $\"EB=BF=8\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "since $\"EO=FO=DO\"$ , angle $\"EAO\"$ = angle $\"DAO\"$ , and $\"AO=AO\"$ .....=> triangles $\"EAO\"$ and $\"DAO\"$ are congruent, then $\"AE=AD=12\"$ \r
\n" ); document.write( "\n" ); document.write( "since $\"EO=FO=DO\"$ , angle $\"DCO\"$ = angle $\"FCO\"$ , and $\"AO=AO\"$ .....=> triangles $\"DCO\"$ and $\"FCO\"$ are congruent, then $\"DC=CF=15\"$ \r
\n" ); document.write( "\n" ); document.write( "since the length of $\"AC=AD%2BDC\"$ , then $\"AC=12%2B15=27\"$ \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );