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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 $J$.

Here is a figure:

Figure illustrating problem

Prove:

  1. $E$, $B$, $D$, $P$ are concyclic
  2. $CJ\perp AO_2$
  • 1
    It's intended that no further reference beyond their definition is made to $G$ and $H$, right?2012-10-26
  • 0
    Yes, $G$ and $H$ are of no use in the problem statement. I don't know if it will be important to the proof or not, because I don't know the answer although I spend some days on it.2012-10-26

1 Answers 1