# How can prove that three circles coaxial?

Let $$(O_a)$$ meets $$(O'_a)$$ at $$A_1$$, $$A_2$$; $$(O_b)$$ meets $$(O'_b)$$ at $$B_1$$, $$B_2$$; $$(O_c)$$ meets $$(O'_c)$$ at $$C_1$$, $$C_2$$ such that $$A_1$$, $$A_2$$, $$B_1$$, $$B_2$$, $$C_1$$, $$C_2$$ lie on a circle. Let $$(O_a)$$ meets $$(O_b)$$ at two points $$A_b, B_a$$; $$(O'_a)$$ meets $$(O'_b)$$ at two points $$A'_b, B'_a$$ then by Bundle theorem we have quadruple $$A_b, B_a, A'_b, B'_a$$ are concyclic; Define similarly we have two quadruples $$\{B_c, C_b, B'_c, C'_b\}$$ and $$\{C_a, A_c, C'_a, C'_b\}$$ are concyclic. I am looking for a proof that three circles $$(A_bB_aA'_bB'_a)$$, $$(B_cC_bB'_cC'_b)$$, $$(C_aA_cC'_aC'_b)$$ are coaxal.