document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207163>Question 1207163</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two circles intersect (a nd b) and share a common chord (cd). the radius of circle a is 10in, radius circle b = 16 in. distance between centers, 22 in. find cd. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844876 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844876\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=10in ALIGN=MIDDLE  ALT=\"r=10in\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" >:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=16in ALIGN=MIDDLE  ALT=\"r=16in\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "distance between centers=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22in ALIGN=MIDDLE  ALT=\"22in\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if we place the center of the circle a on <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >-ais, at point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-11 ALIGN=MIDDLE  ALT=\"-11\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >), than the center of the circle b will be at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=11 ALIGN=MIDDLE  ALT=\"11\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the distance between them is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22in ALIGN=MIDDLE  ALT=\"22in\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now we have equations:\r<BR>\n" );
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document.write( "circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-%28-11%29%29%5E2%2B%28y-0%29%5E2=10%5E2+ ALIGN=MIDDLE  ALT=\"%28x-%28-11%29%29%5E2%2B%28y-0%29%5E2=10%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B11%29%5E2%2By%5E2=100 ALIGN=MIDDLE  ALT=\"%28x%2B11%29%5E2%2By%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "circle<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+b ALIGN=MIDDLE  ALT=\"+b\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%5E2%2B%28y-0%29%5E2=16%5E2+ ALIGN=MIDDLE  ALT=\"%28x-11%29%5E2%2B%28y-0%29%5E2=16%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%5E2%2By%5E2=256 ALIGN=MIDDLE  ALT=\"%28x-11%29%5E2%2By%5E2=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
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document.write( "find intersection points by solving this system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%5E2%2By%5E2=256 ALIGN=MIDDLE  ALT=\"%28x-11%29%5E2%2By%5E2=256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B11%29%5E2%2By%5E2=100 ALIGN=MIDDLE  ALT=\"%28x%2B11%29%5E2%2By%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----------------------------subtract\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%5E2%2By%5E2-%28x%2B11%29%5E2-y%5E2=256-100 ALIGN=MIDDLE  ALT=\"%28x-11%29%5E2%2By%5E2-%28x%2B11%29%5E2-y%5E2=256-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-11%29%5E2-%28x%2B11%29%5E2=156 ALIGN=MIDDLE  ALT=\"%28x-11%29%5E2-%28x%2B11%29%5E2=156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+22x+%2B+121-%28x%5E2+%2B+22x+%2B+121%29=156 ALIGN=MIDDLE  ALT=\"x%5E2+-+22x+%2B+121-%28x%5E2+%2B+22x+%2B+121%29=156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+22x+%2B+121-x%5E2+-22x+-+121=156 ALIGN=MIDDLE  ALT=\"x%5E2+-+22x+%2B+121-x%5E2+-22x+-+121=156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+22x++-22x+=156 ALIGN=MIDDLE  ALT=\"-+22x++-22x+=156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-+44x+=156 ALIGN=MIDDLE  ALT=\"-+44x+=156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=156%2F-44 ALIGN=MIDDLE  ALT=\"x=156%2F-44\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-39%2F11 ALIGN=MIDDLE  ALT=\"x=-39%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "plug it in\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-39%2F11%2B11%29%5E2%2By%5E2=100 ALIGN=MIDDLE  ALT=\"%28-39%2F11%2B11%29%5E2%2By%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6724%2F121%2By%5E2=100 ALIGN=MIDDLE  ALT=\"6724%2F121%2By%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=100-6724%2F121 ALIGN=MIDDLE  ALT=\"y%5E2=100-6724%2F121\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=5376%2F121 ALIGN=MIDDLE  ALT=\"y%5E2=5376%2F121\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=sqrt%285376%2F121%29 ALIGN=MIDDLE  ALT=\"y=sqrt%285376%2F121%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2816+sqrt%2821%29%29%2F11+ ALIGN=MIDDLE  ALT=\"y+=+%2816+sqrt%2821%29%29%2F11+\"   DISABLED_style= \"max-width:90%; height:auto;\" >or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=-+%2816+sqrt%2821%29%29%2F11 ALIGN=MIDDLE  ALT=\"y+=-+%2816+sqrt%2821%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solutions:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-39%2F11 ALIGN=MIDDLE  ALT=\"x+=+-39%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%2816sqrt%2821%29%29%2F11 ALIGN=MIDDLE  ALT=\"y+=+%2816sqrt%2821%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "or\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-39%2F11 ALIGN=MIDDLE  ALT=\"x+=+-39%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+-%2816sqrt%2821%29%29%2F11 ALIGN=MIDDLE  ALT=\"y+=+-%2816sqrt%2821%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "intersection points are\r<BR>\n" );
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document.write( "(<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-39%2F11 ALIGN=MIDDLE  ALT=\"-39%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2816sqrt%2821%29%29%2F11 ALIGN=MIDDLE  ALT=\"%2816sqrt%2821%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-39%2F11 ALIGN=MIDDLE  ALT=\"-39%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-%2816sqrt%2821%29%29%2F11 ALIGN=MIDDLE  ALT=\"-%2816sqrt%2821%29%29%2F11\"   DISABLED_style= \"max-width:90%; height:auto;\" >) \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "distance between is: two times <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" > value \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=2%2A%2816sqrt%2821%29%29%2F11=13.33 ALIGN=MIDDLE  ALT=\"d=2%2A%2816sqrt%2821%29%29%2F11=13.33\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The length of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cd ALIGN=MIDDLE  ALT=\"cd\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.33in ALIGN=MIDDLE  ALT=\"13.33in\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+drawing%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C%0D%0Acircle%28-11%2C0%2C.35%29%2Ccircle%2811%2C0%2C.35%29%2C%0D%0Acircle%28-11%2C0%2C10%29%2Ccircle%2811%2C0%2C16%29%2C+locate%28-15%2C9.5%2Ca%29%2C+locate%2821%2C12%2Cb%29%2C%0D%0Acircle%28-39%2F11%2C%2816sqrt%2821%29%29%2F11%2C.35%29%2Ccircle%28-39%2F11%2C-%2816sqrt%2821%29%29%2F11%2C.35%29%2C%0D%0Alocate%28-39%2F11%2C%2816sqrt%2821%29%29%2F11%2Cc%29%2Clocate%28-39%2F11%2C-%2816sqrt%2821%29%29%2F11%2Cd%29%2C%0D%0Ablue%28line%28-39%2F11%2C%2816sqrt%2821%29%29%2F11%2C-39%2F11%2C-%2816sqrt%2821%29%29%2F11%29%29%2C%0D%0Agraph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+0%29%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );