document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=782788>Question 782788</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If an equilateral triangle is circumscribed about a circle of radius 10 cm, determine the side of the triangle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #476570 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=476570\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C300%2C-20%2C20%2C-15%2C25%2C%0D%0Acircle%280%2C0%2C10%29%2Ctriangle%280%2C20%2C17.3%2C-10%2C-17.3%2C-10%29%2C%0D%0Agreen%28line%280%2C0%2C0%2C-10%29%29%2Cgreen%28line%280%2C0%2C17.3%2C-10%29%29%2C%0D%0Agreen%28rectangle%280%2C-10%2C1%2C-9%29%29%2Clocate%280%2C22%2CB%29%2C%0D%0Alocate%280%2C-4%2Cgreen%2810cm%29%29%2C%0D%0Alocate%2817.3%2C-10%2CA%29%2Clocate%28-17.3%2C-10%2CC%29%2C%0D%0Alocate%280%2C2%2CO%29%2Clocate%280%2C-10%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > Side AC is tangent to the circle, perpendicular to radius OD at the point of tangency (point D).<BR>\n" );
document.write( "We can draw <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6 ALIGN=MIDDLE  ALT=\"6\"   DISABLED_style= \"max-width:90%; height:auto;\" > angles congruent with AOD connecting the center with points of tangency and vertices, and their measures add to <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;\" >,<BR>\n" );
document.write( "so AOD measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=360%5Eo%2F6=60%5Eo ALIGN=MIDDLE  ALT=\"360%5Eo%2F6=60%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Using trigonometry, we know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DA%2FOD=tan%2860%5Eo%29 ALIGN=MIDDLE  ALT=\"DA%2FOD=tan%2860%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DA%2F10cm=sqrt%283%29 ALIGN=MIDDLE  ALT=\"DA%2F10cm=sqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DA=%2810cm%29%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"DA=%2810cm%29%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CD+=+DA ALIGN=MIDDLE  ALT=\"CD+=+DA\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=CA+=+CD%2BDA=+2DA+=2%2A%2810cm%29%2Asqrt%283%29=20%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"CA+=+CD%2BDA=+2DA+=2%2A%2810cm%29%2Asqrt%283%29=20%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Rounding, we get an approximmate value of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2834.64cm%29 ALIGN=MIDDLE  ALT=\"highlight%2834.64cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );