78-Cevian triangle associated with Jacobi Configuration

Let ABC be a triangle, let $\triangle J_aJ_bJ_c$, $\triangle J'_aJ'bJ'_c$ be two Jacobi triangle, $A_0=J_aJ'_a \cap BC$, define $B_0,C_0$ cyclically. Then $AA_0,BB_0,CC_0$ are concurrent