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Found problems: 701

2015 Sharygin Geometry Olympiad, P6
Tags: geometry , symmetry , altitude
Let $AA', BB'$ and $CC'$ be the altitudes of an acute-angled triangle $ABC$. Points $C_a, C_b$ are symmetric to $C' $ wrt $AA'$ and $BB'$. Points $A_b, A_c, B_c, B_a$ are defined similarly. Prove that lines $A_bB_a, B_cC_b$ and $C_aA_c$ are parallel.