For $a)$, All good line concur at incenter For $b)$ All good line concur at center of regular polygon, both is a point that is a center of circle inscribed in triangle or regular polygon

How do you prove it ??

This question must have appeared at least 5 times on the Olympiad forum this year. See http://www.artofproblemsolving.com/community/c6h1188051