<PRE><B>Question 1189474</B>
&lt;br&gt;
All four triangles are similar, because they are right triangles which have acute angles that are congruent.  So&lt;br&gt;
BF/BC=BC/BD&lt;br&gt;
Given BC=40 and CD=9, we can determine BD=41.  Then in similar triangles BFC and BCD&lt;br&gt;
BF/BC=BC/BD
BF/40=40/41
BF=(40/41)*40&lt;br&gt;
That makes FD=(1/41)*40.&lt;br&gt;
Next, BE and FD are the same length, so&lt;br&gt;
EF = (39/41)*40&lt;br&gt;
ANSWER: BF=1560/41</PRE>