Given a triangle
. The points
,
,
divide the circumcircle
of the triangle
into three arcs
,
,
. Let
be a variable point on the arc
, and let
and
be the incenters of the triangles
and
. Prove that the circumcircle of the triangle
intersects the circle
in a fixed point.
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Given a triangle $ABC$. The points $A$, $B$, $C$ divide the circumcircle $\Omega$ of the triangle $ABC$ into three arcs $BC$, $CA$, $AB$. Let $X$ be a variable point on the arc $AB$, and let $O_{1}$ and $O_{2}$ be the incenters of the triangles $CAX$ and $CBX$. Prove that the circumcircle of the triangle $XO_{1}O_{2}$ intersects the circle $\Omega$ in a fixed point.
Školjka