Concurrent lines in a triangle

On side $AB$, $BC$, and $CA$ of a triangle $ABC$ construct squares $ABB_1A_1$, $BCC_1B_2$, and $CAA_2C_2$. Let $P$ be the center of square $BCC_1B_2$. Show that the lines $A_1C$, $A_2B$ and $AP$ are concurrent.

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