Question 42
Let $ABCDE$ be a convex pentagon. Let $A_1$ be the intersection of lines $BD$ and $CE$, let $B_1$ be the intersection of lines $CE$ and $DA$, and define $C_1, D_1, E_1$ similarly. Let $A_2$ be the second intersection point of the circumcircle of triangle $ABD_1$ and the circumcircle of triangle $AEC_1$, let $B_2$ be the second intersection point of the circumcircle of triangle $BCE_1$ and the circumcircle of triangle $BAD_1$, and define $C_2, D_2, E_2$ similarly. Prove that the lines $AA_2, BB_2, CC_2, DD_2, EE_2$ are concurrent.