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.
Školjka