In the triangle
![ABC,](/media/m/8/a/f/8afcbd6e815ca10256c79a5b310e3d67.png)
with
![\angle A = 60 ^{\circ},](/media/m/a/b/8/ab8bcefbb68a68fa21623904ffc06623.png)
a parallel
![IF](/media/m/9/9/4/99490c823319f9160fbc22a10d37c9f8.png)
to
![AC](/media/m/6/4/7/647ef3a5d68f07d59d84afe03a9dc655.png)
is drawn through the incenter
![I](/media/m/3/8/6/38689d6affa9ba35368ca4d3d76ea147.png)
of the triangle, where
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
lies on the side
![AB.](/media/m/7/2/c/72c695f238f1781e4becd2529232f12a.png)
The point
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
on the side
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
is such that
![3BP = BC.](/media/m/7/4/a/74a69131ac8d373b64a69b1d14cd9b03.png)
Show that
%V0
In the triangle $ABC,$ with $\angle A = 60 ^{\circ},$ a parallel $IF$ to $AC$ is drawn through the incenter $I$ of the triangle, where $F$ lies on the side $AB.$ The point $P$ on the side $BC$ is such that $3BP = BC.$ Show that $\angle BFP = \frac{\angle B}{2}.$