In an acute triangle
the points
and
are the feet of the altitudes through
and
respectively. The incenters of the triangles
and
are
and
respectively; the circumcenters of the triangles
and
are
and
respectively. Prove that
and
are parallel.
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In an acute triangle $ABC$ the points $D,E$ and $F$ are the feet of the altitudes through $A,B$ and $C$ respectively. The incenters of the triangles $AEF$ and $BDF$ are $I_1$ and $I_2$ respectively; the circumcenters of the triangles $ACI_1$ and $BCI_2$ are $O_1$ and $O_2$ respectively. Prove that $I_1I_2$ and $O_1O_2$ are parallel.
Školjka