document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=992303>Question 992303</A>: <I><SPAN STYLE=\"word-break: break-all;\"> QUESTION:In circle O, diameter AB is perpendicular to chord CD at E. If CD=20cm, BE=2cm and AE= 4x-2, find the length of the diameter.\r<BR>\n" );
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document.write( "Using the intersecting chord theorem I know how to solve it, however neither values of CE or DE are given and you can't have two variables in an equation so I'm confused. By long shot i thought of using trigonometry but i don't think it's right. Thanks for the help  in advance x  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #611928 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=611928\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the length of your diameter is 4x-2 + 2 = 4x.<BR>\n" );
document.write( "this means your radius is equal to 2x.\r<BR>\n" );
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document.write( "if CD is equal to 20, this means that CE and ED are both equal to 10 because a diameter cuts a chord perpendicular to it into 2 equal segments.\r<BR>\n" );
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document.write( "here's what you have:\r<BR>\n" );
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document.write( "AB = the diameter = 4x.<BR>\n" );
document.write( "AO = a radius = 2x.<BR>\n" );
document.write( "OB = a radius = 2x.\r<BR>\n" );
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document.write( "since EB is equal to 2, then OE must be equal to 2x-2.\r<BR>\n" );
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document.write( "CE is equal to 10<BR>\n" );
document.write( "ED is equal to 10\r<BR>\n" );
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document.write( "OC is equal to 2x because OC is a radius.<BR>\n" );
document.write( "OD is equal to 2x because OD is a radius.\r<BR>\n" );
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document.write( "you have a right triangle formed that is OCE.<BR>\n" );
document.write( "in that triangle:<BR>\n" );
document.write( "OC is the hypotenuse which is equal to 2x.<BR>\n" );
document.write( "OE is one leg which is equal to 2x-2.<BR>\n" );
document.write( "CE is the other leg which is equal to 10.\r<BR>\n" );
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document.write( "by pythagorus, OE^2 + CE^2 = OC^2 which becomes:<BR>\n" );
document.write( "(2x-2)^2 + 10^2 = (2x)^2<BR>\n" );
document.write( "simplify this equation to get:<BR>\n" );
document.write( "4x^2 - 8x + 4 + 100 = 4x^2<BR>\n" );
document.write( "subtract 4x^2 from both sides of the equation to get:<BR>\n" );
document.write( "-8x + 4 + 100 = 0<BR>\n" );
document.write( "add 8x to both sides of the equation to get:<BR>\n" );
document.write( "4 + 100 = 8x<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "104 = 8x<BR>\n" );
document.write( "solve for x to get:<BR>\n" );
document.write( "x = 13.\r<BR>\n" );
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document.write( "if x = 13, then:<BR>\n" );
document.write( "OC = 2x = 26<BR>\n" );
document.write( "OE = 2x-2 = 24<BR>\n" );
document.write( "CE = 10\r<BR>\n" );
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document.write( "by pythagorus, 10^2 + 24^2 = 26^2<BR>\n" );
document.write( "this becomes:<BR>\n" );
document.write( "100 + 576 = 676 which becomes:<BR>\n" );
document.write( "676 = 676<BR>\n" );
document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "you are asked to find the length of the diameter.<BR>\n" );
document.write( "the length of the diameter is 4x which is equal to 4 * 13 which is equal to 52.\r<BR>\n" );
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document.write( "i believe that's your solution.\r<BR>\n" );
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document.write( "here's a picture to help you understand what i'm talking about.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/092602.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the key to solving is to know the geometric relationship that a chord perpendicular to a diameter is cut in half.\r<BR>\n" );
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document.write( "you also needed to determine that the length of the diameters was 4x-2 + 2 which made it equal to 4x.\r<BR>\n" );
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document.write( "you also needed to know that the triangle formed had a hypotenuse that was equal to the radius.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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