Let
be a triangle,
its orthocenter,
its circumcenter, and
its circumradius. Let
be the reflection of the point
across the line
, let
be the reflection of the point
across the line
, and let
be the reflection of the point
across the line
. Prove that the points
,
and
are collinear if and only if
.
%V0
Let $ABC$ be a triangle, $H$ its orthocenter, $O$ its circumcenter, and $R$ its circumradius. Let $D$ be the reflection of the point $A$ across the line $BC$, let $E$ be the reflection of the point $B$ across the line $CA$, and let $F$ be the reflection of the point $C$ across the line $AB$. Prove that the points $D$, $E$ and $F$ are collinear if and only if $OH=2R$.
Školjka