document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=305478>Question 305478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I'm not sure if this is too big a question but if someone could at least point me in the right direction I'd appriciate it.<BR>\n" );
document.write( "Place 3 circles with the same radius, r, with their centers on a horizontal in such a way that the middle circle intersects the left and right circles in exactly 1 point each(like 3 coins, touching, all in a row). Draw a line from the center of the left circle that is tangent to the right circle. This line intersects the middle circle in 2 points. Find the length of the line segment connecting these 2 points in terms of r.<BR>\n" );
document.write( "Ok so I have the picture fine I'm pretty sure about that. In the middle circle i tried drawing radii from the center to the points of the segment i have to find the length of, and i know it's an isosceles triangle but that doesn't help me find the length of that segment. I've also tried right triangles in different areas but nothing i have come up with has helped...once again I'd really appriciate it if someone could at least steer me in the right direction. Thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #218724 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=218724\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Make the origin the center of your first circle (left hand side).<BR>\n" );
document.write( "The center of the middle circle is then (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2R ALIGN=MIDDLE  ALT=\"2R\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and the equation of the middle circle is then,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2R%29%5E2%2By%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28x-2R%29%5E2%2By%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tangent line also starts at (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0 ALIGN=MIDDLE  ALT=\"0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) and has has the formula,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx ALIGN=MIDDLE  ALT=\"y=mx\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tangent line is the base of a right triangle that has a hypotenuse equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4R ALIGN=MIDDLE  ALT=\"4R\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the other side <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The third side is then, by the Pythagorean theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284R%29%5E2-R%5E2=S%5E2 ALIGN=MIDDLE  ALT=\"%284R%29%5E2-R%5E2=S%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E2=16R%5E2-R%5E2=15R%5E2 ALIGN=MIDDLE  ALT=\"S%5E2=16R%5E2-R%5E2=15R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=sqrt%2815%29R ALIGN=MIDDLE  ALT=\"S=sqrt%2815%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The tangent of the angle that the tangent line makes with the x-axis is then equal to opposite side, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" >, over the adjacent side, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2815%29R ALIGN=MIDDLE  ALT=\"sqrt%2815%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is also the slope you need \"m\".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28R%2F%28sqrt%2815%29R%29%29%2Ax ALIGN=MIDDLE  ALT=\"y=%28R%2F%28sqrt%2815%29R%29%29%2Ax\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2Fsqrt%2815%29 ALIGN=MIDDLE  ALT=\"y=x%2Fsqrt%2815%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2=x%5E2%2F15 ALIGN=MIDDLE  ALT=\"y%5E2=x%5E2%2F15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can then plug that into your circle equation to find the two intersection points. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-2R%29%5E2%2By%5E2=R%5E2 ALIGN=MIDDLE  ALT=\"%28x-2R%29%5E2%2By%5E2=R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
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document.write( "Once you have the points, you can use the distance formula to calculate the distance between the points.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5E2=%28x1-x2%29%5E2%2B%28y1-y2%29%5E2 ALIGN=MIDDLE  ALT=\"D%5E2=%28x1-x2%29%5E2%2B%28y1-y2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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