document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101923>Question 1101923</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three curtain rods, viewed from a sideways view, each have a diameter 3 cm, and are bound together by a band. The curtain rods (circles) are placed so there are two on the bottom and one on top of those two, in the middle, and the three resemble a triangle). The band goes around the three rods, but does not follow the shapes of the circles perfectly. The band becomes \"taut\" when it is not touching any part of the circles. Find the length of the band, in cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716549 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=716549\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here is the drawing of the cross section of the rods bundle to go with ikleyn's solution:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C400%2C-2.5%2C2.5%2C-2.3%2C2.7%2C%0D%0Acircle%28-1%2C-0.5774%2C1%29%2Ccircle%281%2C-0.5774%2C1%29%2C%0D%0Agreen%28triangle%28-1%2C-0.5774%2C1%2C-0.5774%2C0%2C1.1547%29%29%2C%0D%0Ablue%28line%28-1%2C-0.5774%2C-1.866%2C-0.0744%29%29%2C%0D%0Ablue%28line%281%2C-0.5774%2C1.866%2C-0.0744%29%29%2C%0D%0Ablue%28line%28-1%2C-0.5774%2C-1%2C-1.5574%29%29%2C%0D%0Ablue%28line%281%2C-0.5774%2C1%2C-1.5574%29%29%2C%0D%0Ablue%28line%280%2C1.1547%2C-0.866%2C1.6547%29%29%2C%0D%0Ablue%28line%280%2C1.1547%2C0.866%2C1.6547%29%29%2C%0D%0Acircle%280%2C1.1547%2C1%29%2Cred%28line%281.866%2C-0.0744%2C0.866%2C1.6547%29%29%2C%0D%0Ared%28line%28-1.866%2C-0.0744%2C-0.866%2C1.6547%29%29%2Cred%28line%28-1%2C-1.5574%2C1%2C-1.5574%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The green triangle connects the centers of the <BR>\n" );
document.write( "The red line segments represent the portions of the band not in contact with the circles.<BR>\n" );
document.write( "The end of those red segments are at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3cm%2F2=1.5cm ALIGN=MIDDLE  ALT=\"3cm%2F2=1.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the center of one of the circles,<BR>\n" );
document.write( "That distance between (red) line and circle center is measured along the blue lines,<BR>\n" );
document.write( "perpendicular to the red lines, of course.<BR>\n" );
document.write( "That makes the green=blue-red quadrilateral a rectangle:<BR>\n" );
document.write( "two congruent blue opposite sides make a parallelogram,<BR>\n" );
document.write( "and a parallelogram with two right angles is a rectangle.<BR>\n" );
document.write( "So, the green and te red segments are all conguent, all 3 cm long.<BR>\n" );
document.write( "Of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > of central angle (and circumference) around each circle,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%5Eo%2B90%5Eo%2B90%5Eo=240%5Eo ALIGN=MIDDLE  ALT=\"60%5Eo%2B90%5Eo%2B90%5Eo=240%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > is covered by<BR>\n" );
document.write( "one angle of the triangle,<BR>\n" );
document.write( "one angle of a rectangle, and<BR>\n" );
document.write( "one angle of another rectangle.<BR>\n" );
document.write( "Along the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo-240%5Eo=120%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo-240%5Eo=120%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > degrees of its circumference,<BR>\n" );
document.write( "each circle is in contact with the bandwrapped around the rod bundle. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );