Question 1186394
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<pre>

There is a general theorem in Geometry, saying that


  +--------------------------------------------------------------------------+         
  | if in a circle two chords, QR and ST, intersect at the interior point U  |
  |                                                                          |
  |              of the circle, then  QU * RU = SU * TU.                     |
  +--------------------------------------------------------------------------+         


In your case, it gives an equation


        6 * 9 = 7 * TU.


From this equation, you find  TU = {{{(6*9)/7}}} = {{{54/7}}} = 7 {{{5/7}}}.    <U>ANSWER</U>
</pre>

Solved.


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Regarding this theorem, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A 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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A 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>, 

in this site.


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


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>".



Save the link to this online textbook together with its description


Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson


to your archive and use it when it is needed.