In an acute-angled triangle
let
be altitudes and
internal bisectors. Denote by
and
the incenter and the circumcentre of the triangle, respectively. Prove that the points
and
are collinear if and only if the points
and
are collinear.
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In an acute-angled triangle $ABC,$ let $AD,BE$ be altitudes and $AP,BQ$ internal bisectors. Denote by $I$ and $O$ the incenter and the circumcentre of the triangle, respectively. Prove that the points $D, E,$ and $I$ are collinear if and only if the points $P, Q,$ and $O$ are collinear.
Školjka