Given a triangle
satisfying
. The incircle of triangle
has center
and touches the sides
and
at the points
and
, respectively. Let
and
be the reflections of the points
and
with respect to
. Prove that the points
,
,
,
lie on one circle.
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Given a triangle $ABC$ satisfying $AC+BC=3\cdot AB$. The incircle of triangle $ABC$ has center $I$ and touches the sides $BC$ and $CA$ at the points $D$ and $E$, respectively. Let $K$ and $L$ be the reflections of the points $D$ and $E$ with respect to $I$. Prove that the points $A$, $B$, $K$, $L$ lie on one circle.
Školjka