document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=344990>Question 344990</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two circles intersect and have a common chord that is 16cm long . the centers are 21cm apart . if the radius of one circle is 10cm ,find the radius of the other circle  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #246823 by </B><A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><B>Edwin McCravy(20060)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Edwin+McCravy><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Edwin+McCravy><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=246823\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C288%2C-11%2C39%2C-18%2C18%2C%0D%0Alocate%280%2C0%2CA%29%2C+locate%2821%2C0%2CB%29%2C+locate%285.5%2C10%2CC%29%2C+locate%285.5%2C-8.5%2CD%29%2C%0D%0Acircle%280%2C0%2C10%29%2C+circle%2821%2C0%2C17%29%2C+line%280%2C0%2C21%2C0%29%2C+line%286%2C8%2C6%2C-8%29%2C%0D%0Alocate%286.5%2C0%2CE%29+%0D%0A%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First we will assume the smaller circle is the one with radius 10.<BR>\n" );
document.write( "We will let the radius of the larger circle be r. We draw in a<BR>\n" );
document.write( "radius of each circle (in green):<BR>\n" );
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document.write( "Then AC = 10, AB=21, BC = r, and CE = 8 since it is half of<BR>\n" );
document.write( "the common chord CD, which is 16.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C288%2C-11%2C39%2C-18%2C18%2C+locate%286.5%2C0%2CE%29%2C%0D%0Alocate%280%2C0%2CA%29%2C+locate%2821%2C0%2CB%29%2C+locate%285.5%2C10%2CC%29%2C+locate%285.5%2C-8.5%2CD%29%2C%0D%0Acircle%280%2C0%2C10%29%2C+circle%2821%2C0%2C17%29%2C+line%280%2C0%2C21%2C0%29%2C+line%286%2C8%2C6%2C-8%29%2C%0D%0Agreen%28line%280%2C0%2C6%2C8%29%2Cline%286%2C8%2C21%2C0%29%2Clocate%28.5%2C5%2C10%29%29%2C+locate%2814%2C6%2Cr%29%2C%0D%0Alocate%286.5%2C4%2C8%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Triangle ACE is a right triangle, so we can find AE by the Pythagorean<BR>\n" );
document.write( "theorem:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AC%5E2+=+AE%5E2%2BCE%5E2 ALIGN=MIDDLE  ALT=\"AC%5E2+=+AE%5E2%2BCE%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E2+=+AE%5E2%2B8%5E2 ALIGN=MIDDLE  ALT=\"10%5E2+=+AE%5E2%2B8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=AE%5E2%2B64 ALIGN=MIDDLE  ALT=\"100=AE%5E2%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36=AE%5E2 ALIGN=MIDDLE  ALT=\"36=AE%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29=AE ALIGN=MIDDLE  ALT=\"sqrt%2836%29=AE\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6=AE ALIGN=MIDDLE  ALT=\"6=AE\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C288%2C-11%2C39%2C-18%2C18%2C+locate%286.5%2C0%2CE%29%2C%0D%0Alocate%280%2C0%2CA%29%2C+locate%2821%2C0%2CB%29%2C+locate%285.5%2C10%2CC%29%2C+locate%285.5%2C-8.5%2CD%29%2C%0D%0Acircle%280%2C0%2C10%29%2C+circle%2821%2C0%2C17%29%2C+line%280%2C0%2C21%2C0%29%2C+line%286%2C8%2C6%2C-8%29%2C%0D%0Agreen%28line%280%2C0%2C6%2C8%29%2Cline%286%2C8%2C21%2C0%29%2Clocate%28.5%2C5%2C10%29%29%2C+locate%2814%2C6%2Cr%29%2C%0D%0Alocate%286.5%2C4%2C8%29%2C+locate%283%2C0%2C6%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<i>(We can see here that the larger circle could not have been the<BR>\n" );
document.write( "one with radius 10, for that would have made BE = 6 which would have<BR>\n" );
document.write( "been shorter than AE.)</i>\r<BR>\n" );
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document.write( "Therefore since AB = 21 and AE = 6\r<BR>\n" );
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document.write( "AB = AE + EB\r<BR>\n" );
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document.write( "21 = 6 + EB\r<BR>\n" );
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document.write( "15 = EB\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C288%2C-11%2C39%2C-18%2C18%2C+locate%286.5%2C0%2CE%29%2C%0D%0Alocate%280%2C0%2CA%29%2C+locate%2821%2C0%2CB%29%2C+locate%285.5%2C10%2CC%29%2C+locate%285.5%2C-8.5%2CD%29%2C%0D%0Acircle%280%2C0%2C10%29%2C+circle%2821%2C0%2C17%29%2C+line%280%2C0%2C21%2C0%29%2C+line%286%2C8%2C6%2C-8%29%2C%0D%0Agreen%28line%280%2C0%2C6%2C8%29%2Cline%286%2C8%2C21%2C0%29%2Clocate%28.5%2C5%2C10%29%29%2C+locate%2814%2C6%2Cr%29%2C%0D%0Alocate%286.5%2C4%2C8%29%2C+locate%283%2C0%2C6%29%2C+locate%2813%2C0%2C15%29%0D%0A%0D%0A+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Triangle CEB is a right triangle, so we can find r by<BR>\n" );
document.write( "the Pythagorean theorem\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=BC%5E2+=+BE%5E2%2BCE%5E2 ALIGN=MIDDLE  ALT=\"BC%5E2+=+BE%5E2%2BCE%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2+=+15%5E2%2B8%5E2 ALIGN=MIDDLE  ALT=\"r%5E2+=+15%5E2%2B8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=225%2B64 ALIGN=MIDDLE  ALT=\"r%5E2=225%2B64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2=289 ALIGN=MIDDLE  ALT=\"r%5E2=289\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28289%29 ALIGN=MIDDLE  ALT=\"r=sqrt%28289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=17cm ALIGN=MIDDLE  ALT=\"r=17cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Edwin</pre> </SPAN>\n" );
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