Circle $\odot O_1$ is tangent with circle $\odot O_2$ at $P$. Two tangent lines $AE$ and $AF$ of circle $\odot O_2$ meets circle $O_1$ at $B$, $G$ and $C$, $H$, respectively. $D$ is the in-center of $\triangle ABC$. $DP$ meets $BC$ at $I$, $EI$ meets $AO_2$ at $J$.
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Prove:
- $E$, $B$, $D$, $P$ are concyclic
- $CJ\perp AO_2$