4 concyclic incenters

[ins-]

There are given two circles - $m$ and $n$. $n$ is internally tangent to $m$ at the point $T$. $p$ and $q$ are two tangents to $n$ with tangency points $C_1$ and $C_2$ respectively. $A_1$ and $B_1$ are the intersection points of $p$ with the circle $m$. $A_2$ and $B_2$ are the intersection points of $q$ with $m$. Prove that incenters of the triangles $TA_1C_1$, $TB_1C_1$, $TA_2C_2$, $TB_2C_2$ are concyclic.

[Dimoniada]

After 2 weeks papers research, it seems to be wrong statement... It's obvious bring out in any proper pic...

[ins-]

Oh ... I'm sorry. I knew that but I forgot to tell it.

-- Пт фев 08, 2013 00:09:01 --

Indeed ... this mistake shows I (re)discovered most of the problems I post.