Y by Adventure10, Mango247
Let an acute-angled triangle
's circumcircle is
.
's tangent from
and
intersects at point
. A line, lies
and parallel to
intersects with
at points
and
, intersect with
at point
. Prove that
![$$[DF]=[FE]$$](//latex.artofproblemsolving.com/0/4/d/04d631aea099c3300d230937e13e59a743140344.png)







![$[AB]$](http://latex.artofproblemsolving.com/a/d/a/ada6f54288b7a2cdd299eba0055f8c8d19916b4b.png)



![$[AC]$](http://latex.artofproblemsolving.com/0/9/3/0936990e6625d65357ca51006c08c9fe3e04ba0c.png)

![$$[DF]=[FE]$$](http://latex.artofproblemsolving.com/0/4/d/04d631aea099c3300d230937e13e59a743140344.png)
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