2016 Philippine MO
Pentagon 
is inscribed in a circle. Its diagonals 
and 
intersect at 
. The bisectors of 
and 
intersect at 
. Let 
intersect at 
, let 
intersect at 
, and let 
intersect 
at 
. If 
is cyclic and ![\[JA \cdot FC \cdot GH = JD \cdot FB \cdot GI,\]](//latex.artofproblemsolving.com/7/a/4/7a4e08d94274ca0c32378a4bff421026ca561243.png)
prove that , and 
are collinear.
is inscribed in a circle. Its diagonals 
and 
intersect at 
. The bisectors of 
and 
intersect at 
. Let 
intersect at 
, let 
intersect at 
, and let 
intersect 
at 
. If 
is cyclic and ![\[JA \cdot FC \cdot GH = JD \cdot FB \cdot GI,\]](http://latex.artofproblemsolving.com/7/a/4/7a4e08d94274ca0c32378a4bff421026ca561243.png)
prove that , and 
are collinear.
