Let
be a circumscribed quadrilateral. Let
be a line through
which meets the segment
in
and the line
in
. Denote by
,
and
the incenters of
,
and
, respectively. Prove that the orthocenter of
lies on
.
Proposed by Nikolay Beluhov, Bulgaria
%V0
Let $ABCD$ be a circumscribed quadrilateral. Let $g$ be a line through $A$ which meets the segment $BC$ in $M$ and the line $CD$ in $N$. Denote by $I_1$, $I_2$ and $I_3$ the incenters of $\triangle ABM$, $\triangle MNC$ and $\triangle NDA$, respectively. Prove that the orthocenter of $\triangle I_1I_2I_3$ lies on $g$.
Proposed by Nikolay Beluhov, Bulgaria
Školjka