document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=8853>Question 8853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> you are given rectangle abcd. how many distinct circles in the same plane of the rectangle have a diameter both of whose endpoints are vertices abcd? what is the sum of the diameters of all of the circles? be sure to answer both questions.\r<BR>\n" );
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document.write( "A-----------------------------D<BR>\n" );
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document.write( "                              5 cm.                              <BR>\n" );
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document.write( "B-----------------------------C<BR>\n" );
document.write( "         12 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4854 by </B><A HREF=/tutors/aboutme.mpl?userid=khwang><B>khwang(438)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=khwang><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=4854\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  I think you mean AB = CD = 5,   AD= BC = 12.\r<BR>\n" );
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document.write( " Let AC  and BD intersect at O, we see that AO=CO= BO=DO .<BR>\n" );
document.write( " [Set it be r]<BR>\n" );
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document.write( " The circle centered at O with radius r passing through A,B,C & D.<BR>\n" );
document.write( " This is the unique circle (in the same plane of the rectangle)<BR>\n" );
document.write( " have two diameters AC & BD  whose endpoints are vertices A,B,C & D.\r<BR>\n" );
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document.write( " By Pyth. theorem AC^2 = AB^2 + BC^2 = 169,so AC = 13 cm (=BD).<BR>\n" );
document.write( " Hence, the sum the diameters = 26 cm<BR>\n" );
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document.write( " Since there are infinitely many diamaters in circle, the question<BR>\n" );
document.write( " should not ask \"what is the sum of the diameters of all of the circles?\"<BR>\n" );
document.write( " in this unreasonable way.\r<BR>\n" );
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document.write( " Kenny<BR>\n" );
document.write( " </SPAN>\n" );
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