document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1087159>Question 1087159</A>: <I><SPAN STYLE=\"word-break: break-all;\"> two circles of radii 5cm and 3cm have their centres 10cm apart draw the dct to the circles diagram<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #701448 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=701448\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Searching for dct to two circles, I found it to stand for \"direct common tangent\",<BR>\n" );
document.write( "and I found that phrase to mean tangent common to both circles that does not cross the line connecting the circles' centers between the centers.<BR>\n" );
document.write( "There is two of those, of course,<BR>\n" );
document.write( "and they remind you of a belt wrapped around two pulleys.<BR>\n" );
document.write( "I found that indirect common tangents would be the ones that cross between the circles.<BR>\n" );
document.write( "CIRCLES (with the line connecting their centers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28600%2C300%2C-10.5%2C16.5%2C-6.75%2C6.75%2C%0D%0Agreen%28arrow%283%2C0%2C20%2C0%29%29%2Cgreen%28arrow%283%2C0%2C-14%2C0%29%29%2C%0D%0Acircle%28-5%2C0%2C0.1%29%2Ccircle%28-5%2C0%2C5%29%2C%0D%0Acircle%285%2C0%2C0.1%29%2Ccircle%285%2C0%2C3%29%2C%0D%0Alocate%28-7.7%2C0%2C5%29locate%28-2.7%2C0%2C5%29%2C%0D%0Alocate%280.8%2C0%2C2%29%2Clocate%283.3%2C0%2C3%29%2Clocate%286.3%2C0%2C3%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Drawing that with pencil, ruler, and compass,<BR>\n" );
document.write( "and adding the direct common tangents with a straightedge or ruler would be easy.<BR>\n" );
document.write( "Calculating coordinates for the points of tangency is not so easy.<BR>\n" );
document.write( "Here is the drawing with the direct common tangents added.<BR>\n" );
document.write( "CIRCLES (with the line connecting their centers:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28800%2C300%2C-10.5%2C25.5%2C-6.75%2C6.75%2C%0D%0Acircle%28-5%2C0%2C0.1%29%2Ccircle%28-5%2C0%2C5%29%2C%0D%0Acircle%285%2C0%2C0.1%29%2Ccircle%285%2C0%2C3%29%2C%0D%0Alocate%28-7.7%2C0%2C5%29locate%28-2.7%2C0%2C5%29%2Clocate%2813%2C0%2C12%29%2C%0D%0Alocate%280.8%2C0%2C2%29%2Clocate%283.3%2C0%2C3%29%2Clocate%286.3%2C0%2C3%29%2C%0D%0Alocate%285.25%2C1.67%2C3%29%2Clocate%28-4.46%2C2.65%2C5%29%2C%0D%0Ared%28triangle%28-5%2C0%2C-4%2C4.9%2C20%2C0%29%29%2C%0D%0Ared%28triangle%285%2C0%2C5.6%2C2.94%2C20%2C0%29%29%2C%0D%0Ared%28line%285.38%2C2.35%2C5.97%2C2.23%29%29%2C%0D%0Ared%28line%286.09%2C2.82%2C5.97%2C2.23%29%29%2C%0D%0Ared%28line%28-4.12%2C4.31%2C-3.53%2C4.19%29%29%2C%0D%0Ared%28line%28-3.53%2C4.19%2C-3.41%2C4.78%29%29%2C%0D%0Ared%28arrow%28-4%2C4.9%2C-10.4%2C6.22%29%29%2C%0D%0Ared%28arrow%2820%2C0%2C25%2C-1.08%29%29%2C%0D%0Ared%28arrow%28-4%2C-4.9%2C-10.4%2C-6.22%29%29%2C%0D%0Ared%28arrow%2820%2C0%2C25%2C1.08%29%29%2C%0D%0Ared%28triangle%28-5%2C0%2C-4%2C-4.9%2C20%2C0%29%29%2C%0D%0Agreen%28arrow%283%2C0%2C30%2C0%29%29%2Cgreen%28arrow%283%2C0%2C-14%2C0%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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