document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=328656>Question 328656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A pentagon is inscribed in a circle. What is a possible number of the pentagon's diagonals that can be diameters of the circle? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #235475 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=235475\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a pentagon has 5 sides.\r<BR>\n" );
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document.write( "We are assuming regular pentagons (each side is equal and all central angles are the same).\r<BR>\n" );
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document.write( "It has 5 central angles.\r<BR>\n" );
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document.write( "Each central angle is equal to 360 / 5 = 72 degrees.\r<BR>\n" );
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document.write( "A circumscribed circle will have the same center as the pentagon.\r<BR>\n" );
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document.write( "In order for a diagonal of the pentagon to be a diameter of the circle, it must form a straight line through the center of the pentagon.\r<BR>\n" );
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document.write( "This means that multiples of each central angle must equal 180 degrees.\r<BR>\n" );
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document.write( "This doesn't happen with a pentagon because an angle of 72 cannot be divided equally into 180.\r<BR>\n" );
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document.write( "The answer is that the possible number of the pentagon's diagonals that can also be a diameter of the circumscribed circle is zero.\r<BR>\n" );
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