Let
be a triangle with incenter
and let
,
and
be the incenters of the triangles
,
and
, respectively. Let the triangle
be equilateral. Prove that
is equilateral too.
Proposed by Mirsaleh Bahavarnia, Iran
%V0
Let $ABC$ be a triangle with incenter $I$ and let $X$, $Y$ and $Z$ be the incenters of the triangles $BIC$, $CIA$ and $AIB$, respectively. Let the triangle $XYZ$ be equilateral. Prove that $ABC$ is equilateral too.
Proposed by Mirsaleh Bahavarnia, Iran
Školjka