71-A line through H

Let $ABC$ be a triangle, $B_a,C_a$ lie on $BC; C_b,B_c$ lie on $CA,BA$ respectively. Such that two circles $(BB_aB_c),(CC_aC_b)$ tangent at $P$ on the circumcircle and $B_cB_a \perp AC, C_aC_b \perp AB$. Denote $A_b=B_aB_c \cap AC, A_c=C_aC_b \cap AB$. Show that: $A_bA_c$ through the orthoenter of the triangle $ABC$. $M=B_cC_b \cap AO$, $M$ lie on circumcircle of $ABC$