document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=146646>Question 146646</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle has a chord of length 8 that is tangent to a smaller, concentric circle.Find the area between the two circles:\r<BR>\n" );
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document.write( "a) 16    (note each of the answers listed have a pie sign next to them.)<BR>\n" );
document.write( "b) 9<BR>\n" );
document.write( "c) 24<BR>\n" );
document.write( "d) 36<BR>\n" );
document.write( "e) none \r<BR>\n" );
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document.write( "Again THANK YOU !!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107081 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107081\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> It always helps to draw a picture\r<BR>\n" );
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document.write( "note: \"R\" is the radius of the larger circle and \"r\" is radius of the smaller circle. Also, I divided the chord in half. \r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"http://www.flickr.com/photos/7963298@N08/2617453180/\" title=\"circle by jim_thompson5910, on Flickr\"><IMG STYLE=\"max-width:80%;\" src=\"http://farm4.static.flickr.com/3120/2617453180_844ea2e243.jpg\" width=\"487\" height=\"471\" alt=\"circle\" /></a>\r<BR>\n" );
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document.write( "From the picture, we can see that the radius R is the hypotenuse of the triangle with legs of \"r\" and 4. So this means\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%5E2%2Br%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"4%5E2%2Br%5E2=R%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=16%2Br%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"16%2Br%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16=R%5E2-r%5E2 ALIGN=MIDDLE  ALT=\"16=R%5E2-r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2 ALIGN=MIDDLE  ALT=\"r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-r%5E2=16 ALIGN=MIDDLE  ALT=\"R%5E2-r%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now the area of the larger circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%2AR%5E2 ALIGN=MIDDLE  ALT=\"A=pi%2AR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the area of the smaller circle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Since we want the area between the two circles, we must subtract the two areas to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AR%5E2-pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2AR%5E2-pi%2Ar%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=pi%28R%5E2-r%5E2%29 ALIGN=MIDDLE  ALT=\"pi%28R%5E2-r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out the GCF <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi ALIGN=MIDDLE  ALT=\"pi\"   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=pi%2816%29 ALIGN=MIDDLE  ALT=\"pi%2816%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-r%5E2=16 ALIGN=MIDDLE  ALT=\"R%5E2-r%5E2=16\"   DISABLED_style= \"max-width:90%; height:auto;\" >. In other words, replace <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2-r%5E2 ALIGN=MIDDLE  ALT=\"R%5E2-r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > with 16\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16pi ALIGN=MIDDLE  ALT=\"16pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms\r<BR>\n" );
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document.write( "So the area between the two circles is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16pi ALIGN=MIDDLE  ALT=\"16pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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