Let be the incenter of triangle . Let and be the points of tangency of the incircle of with and , respectively. The line passes through and is parallel to . The lines and intersect at the points and . Prove that is acute.
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Let $I$ be the incenter of triangle $ABC$. Let $K,L$ and $M$ be the points of tangency of the incircle of $ABC$ with $AB,BC$ and $CA$, respectively. The line $t$ passes through $B$ and is parallel to $KL$. The lines $MK$ and $ML$ intersect $t$ at the points $R$ and $S$. Prove that $\angle RIS$ is acute.
Izvor: Međunarodna matematička olimpijada, shortlist 1998
Školjka 
be the incenter of triangle 
. Let 
and 
be the points of tangency of the incircle of 
and 
, respectively. The line 
passes through 
and is parallel to 
. The lines 
and 
intersect 
and 
. Prove that 
is acute.