IMO Shortlist 2005 problem G1
Dodao/la:
arhiva2. travnja 2012. 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.
%V0
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.
Izvor: Međunarodna matematička olimpijada, shortlist 2005
Školjka 
