document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=839555>Question 839555</A>: <I><SPAN STYLE=\"word-break: break-all;\"> given a circle, draw two chords who's lengths are in the ratio 1:2 and who's distances from the center are in the ration 2:1. Find the length of each chord in terms of the radius 'r' of the circle. Find their lengths if r = 10 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #505847 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=505847\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> given a circle, draw two chords who's lengths are in the ratio 1:2<BR>\n" );
document.write( " and who's distances from the center are in the ration 2:1.<BR>\n" );
document.write( " Find the length of each chord in terms of the radius 'r' of the circle.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A right triangles formed by the chords, with sides: half the chord length,<BR>\n" );
document.write( "distance from the center, and the radius, which is the hypotenuse.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "As I examine these, it's apparent that the two triangles are indentical,<BR>\n" );
document.write( "one triangle the distance from the center is the longer side and the other<BR>\n" );
document.write( "triangle the long side is half the length of the longer chord.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "On the right triangle let the shorter leg = 2, the longer leg = 2s<BR>\n" );
document.write( "The chord will be twice the length of the legs<BR>\n" );
document.write( "Find s in terms of r<BR>\n" );
document.write( "s^2 + (2s)^2 = r^2<BR>\n" );
document.write( "s^2 + 4s^2 = r^2<BR>\n" );
document.write( "5s^2 = r^2<BR>\n" );
document.write( "s^2 = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2F5 ALIGN=MIDDLE  ALT=\"r%5E2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "s = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The shorter chord = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%28r%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"2sqrt%28r%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The longer chord = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%28r%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"4sqrt%28r%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"Find their lengths if r = 10 cm.\"<BR>\n" );
document.write( "The shorter chord: <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%2810%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"2sqrt%2810%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2sqrt%2820%29 ALIGN=MIDDLE  ALT=\"2sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 8.94 cm<BR>\n" );
document.write( "The longer chord: <BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%2810%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"4sqrt%2810%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%2820%29 ALIGN=MIDDLE  ALT=\"4sqrt%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 17.89 cm\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The longer chord = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4sqrt%28r%5E2%2F5%29 ALIGN=MIDDLE  ALT=\"4sqrt%28r%5E2%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ":\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );