document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087375>Question 1087375</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Show that the circles x^2 + y^2 - 16x - 20y + 115 = 0 and x^2 + y^2 + 8x - 10y + 5 = 0 are tangent and fine the point of tangency </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701648 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52805)</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=701648\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
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document.write( "The first circle has the center at (x,y) = (8,10) and the radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-115+%2B+64+%2B+100%29 ALIGN=MIDDLE  ALT=\"sqrt%28-115+%2B+64+%2B+100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2849%29 ALIGN=MIDDLE  ALT=\"sqrt%2849%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7 (make completing the squares).\r\n" );
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document.write( "The second circle has the center at (x,y) = (-4,5) and the radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28-5+%2B+16+%2B+25%29 ALIGN=MIDDLE  ALT=\"sqrt%28-5+%2B+16+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2836%29 ALIGN=MIDDLE  ALT=\"sqrt%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 6 (do the same).\r\n" );
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document.write( "The distance between the centers is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%288-%28-4%29%29%5E2%2B%2810-5%29%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28%288-%28-4%29%29%5E2%2B%2810-5%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28144+%2B+25%29 ALIGN=MIDDLE  ALT=\"sqrt%28144+%2B+25%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28169%29 ALIGN=MIDDLE  ALT=\"sqrt%28169%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 13 = 7 + 6, \r\n" );
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document.write( "exactly as the sum of the radii.\r\n" );
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document.write( "So, we have external touching in this case.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "On using completing the squares to transform a general equation of a circle to its standard form see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Standard-equation-of-a-circle.lesson>Standard equation of a circle</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Find-the-equation-of-the-circle-given-by-its-center-and-tauching-a-given-line.lesson>Find the standard equation of a circle</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/General-equation-of-a-circle.lesson>General equation of a circle</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Transform-general-eqn-of-a-circle-to-the-standard-form-by-completing-the-squares.lesson>Transform general equation of a circle to the standard form by completing the squares</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Quadratic-relations-and-conic-sections/Identify-elements-of-a-circle-given-by-its-general-equation.lesson>Identify elements of a circle given by its general equation</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook in ALGEBRA-II in this site\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/complex/ALGEBRA-II-YOUR-ONLINE-TEXTBOOK.lesson>ALGEBRA-II - YOUR ONLINE TEXTBOOK</A>.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic <BR>\n" );
document.write( "\"<U>Conic sections: Ellipses. Definition, major elements and properties. Solved problems</U>\".\r<BR>\n" );
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document.write( " </SPAN>\n" );
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