Can you provide a proof for the following claim?
Claim. Given bicentric pentagon. Consider the triangle whose sides are two diagonals drawn from the same vertex and side of pentagon opposite from that vertex.Then, center of excircle of this triangle which touches side of pentagon, the vertex of pentagon opposite to that side and the incenter of the pentagon formed by diagonals are collinear.
GeoGebra applet that demonstrates this claim can be found here.