document.write( "Question 1120521: A semicircle with center O and diameter CD is drawn. AB is a chord in it and also another semicircle drawn with AB as diameter intersects CD at E and F respectively. CE=3, EF=7 and FD=2, find AB^2. \n" ); document.write( "
Algebra.Com's Answer #737176 by Alex.33(110)\"\" \"About 
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\n" ); document.write( "\n" ); document.write( "since CE=3, EF=7, FD=2
\n" ); document.write( "the radius of circle O is (3+7+2)/2=6
\n" ); document.write( "that is to say OC=OD=OA=6.
\n" ); document.write( "Therefore, EH=3, OF=4.\r
\n" ); document.write( "\n" ); document.write( "since O' is the center of the smaller circle(circle O')
\n" ); document.write( "O'A=O'B=O'E=O'F.
\n" ); document.write( "hence EH=HF=1/2EF=3.5
\n" ); document.write( "So OH=5.\r
\n" ); document.write( "\n" ); document.write( "Assume AB=x. O'A=x/2.
\n" ); document.write( "In right triangle AOO': OO'^2+(x/2)^2=6^2.
\n" ); document.write( "In right triangle O'OH: OO'^2=O'H^2+(0.5)^2
\n" ); document.write( "In right triangle O'HF: O'H^2+(3.5)^2=(x/2)^2.
\n" ); document.write( "Solve the equation set for x(as you can see OO' and O'H can be eliminated through substitution)
\n" ); document.write( "And then you get x. square it and you obtain AB^2.\r
\n" ); document.write( "\n" ); document.write( "Enjoy!\r
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