Let
be an acute triangle with circumcircle
. Let
be a tangent line to
, and let
and
be the lines obtained by reflecting
in the lines
,
and
, respectively. Show that the circumcircle of the triangle determined by the lines
and
is tangent to the circle
.
Proposed by Japan
%V0
Let $ABC$ be an acute triangle with circumcircle $\Gamma$. Let $\ell$ be a tangent line to $\Gamma$, and let $\ell_a, \ell_b$ and $\ell_c$ be the lines obtained by reflecting $\ell$ in the lines $BC$, $CA$ and $AB$, respectively. Show that the circumcircle of the triangle determined by the lines $\ell_a, \ell_b$ and $\ell_c$ is tangent to the circle $\Gamma$.
Proposed by Japan
Školjka