<PRE><B>Question 1150432</B>
&lt;br&gt;
The statement of the problem is faulty; but the intent is clear.  FC is a radius, not a diameter; let G be the point on the large circle that makes FG a diameter.&lt;br&gt;
Let H be the other point of intersection of the small circle with diameter FG.&lt;br&gt;
Let x be the length of segment CD.&lt;br&gt;
Since BD = 9, the radius of the large circle is x+9.  In particular, AC = 9&lt;br&gt;
Since EF = 5, CE = CH = x+4..&lt;br&gt;
AD and EH are chords of the small circle, intersecting at C.  From the theorem about the lengths of the pieces of two intersecting chords in a circle,&lt;br&gt;
{{{x(x+9) = (x+4)(x+4)}}}
{{{x^2+9x = x^2+8x+16}}}
{{{x = 16}}}&lt;br&gt;
The diameter of the small circle is x + (x+9) = 2x+9 = 41.&lt;br&gt;
So the radius of the small circle is 20.5.&lt;br&gt;

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