document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1112853>Question 1112853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A quadrilateral circumscribing a circle has 3 sides; 5 inches, 4 inches and 5.74 inches. Find the fourth side if the radius of the circle is 2.5 inches. Find also the area of the quadrilateral. Please explain. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #727896 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=727896\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For the quadrilateral in the sketch below, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d=6.74in ALIGN=MIDDLE  ALT=\"d=6.74in\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C325%2C-3.5%2C4.5%2C-3%2C3.5%2C%0D%0Acircle%280%2C0%2C2.5%29%2C%0D%0Aline%28-2.815%2C-2.5%2C1.185%2C-2.5%29%2C%0D%0Aline%28-2.815%2C-2.5%2C-2.137%2C3.2%29%2C%0D%0Aline%284.35%2C1.37%2C1.185%2C-2.5%29%2C%0D%0Aline%284.35%2C1.37%2C-2.137%2C3.2%29%2C%0D%0Alocate%28-3.5%2C0.4%2Ca=5in%29%2C%0D%0Alocate%28-0.9%2C-2.5%2Cb=4in%29%2C%0D%0Alocate%282.8%2C-0.6%2Cc=5.75in%29%2C%0D%0Alocate%281.1%2C2.6%2Cd%29%2C%0D%0Acircle%280%2C0%2C0.05%29%2Clocate%280.7%2C0%2Cgreen%28r=2.5in%29%29%2C%0D%0Agreen%28triangle%280%2C0%2C2.5%2C0%2C0%2C0%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The Pitot theorem says that for a circumscribed quadrilateral with side lengths a, b, c and d in that order,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bc=b%2Bd=%28a%2Bb%2Bc%2Bd%29%2F2=s=semiperimeter ALIGN=MIDDLE  ALT=\"a%2Bc=b%2Bd=%28a%2Bb%2Bc%2Bd%29%2F2=s=semiperimeter\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(In words, the sum of lengths of opposite sides is the semiperimeter).<BR>\n" );
document.write( "Then, the area is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K=r%2As ALIGN=MIDDLE  ALT=\"K=r%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" >=radius of incircle,<BR>\n" );
document.write( "but <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=K%3C=sqrt%28abcd%29 ALIGN=MIDDLE  ALT=\"K%3C=sqrt%28abcd%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The question did not state that the side length were given in order going around the quadrilateral,<BR>\n" );
document.write( "but if we assume that another pair of sides are opposite,<BR>\n" );
document.write( "the inequality above is not true,<BR>\n" );
document.write( "meaning that a circumscribed quadrilateral side lengths could be<BR>\n" );
document.write( "5, 4, 5.74, and 3.26, or<BR>\n" );
document.write( "5, 4, 5.74, and 4.74, but then the circle would have to be smaller.<BR>\n" );
document.write( " </SPAN>\n" );
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