document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1186394>Question 1186394</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this problem, I would really appreciate it. In ⊙M, chords QR and ST intersect at U. What is TU if QU = 6, RU = 9, and SU = 7? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #817293 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52803)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=817293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
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document.write( "There is a general theorem in Geometry, saying that\r\n" );
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document.write( "  | if in a circle two chords, QR and ST, intersect at the interior point U  |\r\n" );
document.write( "  |                                                                          |\r\n" );
document.write( "  |              of the circle, then  QU * RU = SU * TU.                     |\r\n" );
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document.write( "In your case, it gives an equation\r\n" );
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document.write( "        6 * 9 = 7 * TU.\r\n" );
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document.write( "From this equation, you find  TU = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2A9%29%2F7 ALIGN=MIDDLE  ALT=\"%286%2A9%29%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=54%2F7 ALIGN=MIDDLE  ALT=\"54%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 7 <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F7 ALIGN=MIDDLE  ALT=\"5%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" >.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( "Regarding this theorem, &nbsp;see the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Circles/The-parts-of-chords-intersecting-inside-a-circle.lesson>The parts of chords that intersect inside a circle</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-chords-that-intersect-within-a-circle.lesson>Solved problems on chords that intersect within a circle</A>, \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "Also, &nbsp;you have this free of charge online textbook on Geometry\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;<A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> \r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "The referred lessons are the part of this online textbook under the topic &nbsp;\"<U>Properties of circles, inscribed angles, chords, secants and tangents </U>\".\r<BR>\n" );
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document.write( "Save the link to this online textbook together with its description\r<BR>\n" );
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document.write( "Free of charge online textbook in GEOMETRY<BR>\n" );
document.write( "https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson\r<BR>\n" );
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document.write( "to your archive and use it when it is needed.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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