document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044489>Question 1044489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circle of radius 1 unit has an equilateral triangle PQR inscribed in it. The points S and T are points on the circle such that QRST is a rectangle. Find the area, in square units, of the rectangle.\r<BR>\n" );
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document.write( "I would very much appreciate it if you answered. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659797 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=659797\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\"><BR>\n" );
document.write( "See diagram.\r<BR>\n" );
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document.write( " <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=solver91311&illustration_name=EquilateralInscribed.jpg\">\r<BR>\n" );
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document.write( "Construct PM perpendicular to RQ\r<BR>\n" );
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document.write( "Since PQR is equilateral, ROM must be equilateral, therefore RM measures 1.  Since RQ is perpendicular to PM, RQ must bisect angle ORM. Therefore triangle RMN is 30-60-90.  So MN measures 1/2, and RN measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \frac{\sqrt{3}}{2}\">.  RN is half of RQ, so RQ measures <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{3}\">.  RN also bisects OM, so OM must measure 1/2.  By symmetrical analysis, OL must measure 1/2.\r<BR>\n" );
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document.write( "So the width is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 1\"> and the length is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{3}\">, therefore the area is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \sqrt{3}\"> units.\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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