Question 1116742
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I will answer <U>question 1 only</U>.


<pre>
Use the Theorem:

    If two chords intersect in the interior of a circle,  then the product the measures of the segments the intersection point 
    divides each chord is the same.

    See the lesson &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> in this site. 


Then you have  |AF|*|BF| = |EF|*|GF|,   or   8*6 = 2*|EF|,   which implies

|EF| = {{{(8*6)/2}}} = 24 units.
</pre>

Solved.


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In this site, &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> 


The referred lesson is 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.



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