document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992326>Question 992326</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this! Show that the two circles (x - 3)^2 + (y-4)^2 = 25 and (x-1)^2 + (y-5/2)^2 =225/4. touch each other. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611974 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611974\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "Please help me with this! Show that the two circles (x - 3)^2 + (y-4)^2 = 25 and (x-1)^2 + (y-5/2)^2 =225/4. touch each other.<BR>\n" );
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document.write( "The first equation is for the circle of the radius &nbsp;r = 5&nbsp; with the center at the point &nbsp;(x,y) = (3,4).\r<BR>\n" );
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document.write( "The second equation is for the circle of the radius &nbsp;R = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15%2F2 ALIGN=MIDDLE  ALT=\"15%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7.5 ALIGN=MIDDLE  ALT=\"7.5\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;with the center at the point &nbsp;(x,y) = (1,&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F2 ALIGN=MIDDLE  ALT=\"5%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >) = (1, 2.5).\r<BR>\n" );
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document.write( "The distance between the centers is &nbsp;d = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%283-1%29%5E2+%2B+%284-2.5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%283-1%29%5E2+%2B+%284-2.5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282%5E2%2B1.5%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%282%5E2%2B1.5%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%284+%2B+2.25%29 ALIGN=MIDDLE  ALT=\"sqrt%284+%2B+2.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%286.25%29 ALIGN=MIDDLE  ALT=\"sqrt%286.25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5 ALIGN=MIDDLE  ALT=\"2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Notice that the second circle is larger than the first one, &nbsp;and the center of the first circle is located \r<BR>\n" );
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document.write( "inside of the second circle. &nbsp;See the <U>Figure</U> below.\r<BR>\n" );
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document.write( "Now notice that R = d + r: &nbsp;&nbsp;7.5 = 2.5 + 5.\r<BR>\n" );
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document.write( "It means that the first circle touches the second one from the inside.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28+330%2C+330%2C+-7.5%2C+10.5%2C+-5.5%2C+10.5%2C%0D%0A+++++++++++grid%281%29%2C%0D%0A+++++++++++circle+%283%2C+4%2C+5%29%2C%0D%0A+++++++++++circle+%283%2C+4%2C+0.2%29%2C%0D%0A+++++++++++red%28circle+%281%2C+5%2F2%2C+15%2F2%29%29%2C++++++++++%0D%0A+++++++++++red%28circle+%281%2C+5%2F2%2C+0.2%29%29%0D%0A%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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