First we prove that there are $4$ concurrent lines out of the lines $a_1,a_2,.....,a_{100} $. suppose that there are no such $4$ lines. WlOG, the lines in each triple $(a_1,a_2,a_3), (a_4,a_5,a_6) $ are concurrents. then consider the sets $(a_1, a_2, a_4,a_5, a_i) $ for $7\le i\le11$ since there is a concurrent triple in each set, hence there are $4$ concurrent lines. Now relabel the lines again and assume that the lines $a_1,a_2,a_3,a_4 $ are concurrent at $P$. and suppose that $a_5,a_6$ don't pass through $P$ and concur at $Q$. Let $a_x$ be an arbitrary line, clearly there is $1\le i\le 4$ such that $a_x$ doesn't pass through any of $a_i\cap a_5, a_i\cap a_6$, WlOG $i=1$. consider the sets $ (a1, a_i, a_4,a_5,a_x) 2\le i\le 4 $ we get that $a_x$ pass through at least one of $(P, Q) $.