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 #611975 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=611975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the two circles are:<BR>\n" );
document.write( "(x-3)^2 + (y-4)^2 = 25<BR>\n" );
document.write( "(x-1)^2 + (y-5/2)^2 = 225/4\r<BR>\n" );
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document.write( "if they touch, then the tangent line to each circle will pass through the point that they touch at.\r<BR>\n" );
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document.write( "the radius of each circle will be perpendicular to the tangent line at that point.\r<BR>\n" );
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document.write( "this means the two radii will form a straight line that goes through the point of tangency and will intersect both circles at the point of tangency.\r<BR>\n" );
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document.write( "the line will be a straight line formed by the line segment between the two centers of the cirfcle.\r<BR>\n" );
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document.write( "the centers of each circle are (3,4) and (1,(5/2)\r<BR>\n" );
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document.write( "using these two points, you get a straight line with the equation of y = 3/4 * x + 7/4.\r<BR>\n" );
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document.write( "that line should intereset with both circles at the same point.\r<BR>\n" );
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document.write( "i solved it graphically to see that the point of intersection is (7,7).\r<BR>\n" );
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document.write( "that graph is shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092603.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "it should be able to be solved algebraically but i didn't do it because i ran out of time and it's messy.\r<BR>\n" );
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document.write( "i did verify algebraically that the point (7,7) satisfies both equations, so there's no question that is the point of intersection of the two circles.\r<BR>\n" );
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document.write( "you would probably want to solve the intersection of that line with each equation using the substitution method.\r<BR>\n" );
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document.write( "graphing was much easier.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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