Let the incircle
of the triangle
touch its side
at
. Let the line
intersect
at
and denote the excentre of
opposite to
by
. Let
and
be the midpoints of
and
respectively.
Prove that the points
,
,
, and
are concyclic.
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Let the incircle $k$ of the triangle $ABC$ touch its side $BC$ at $D$. Let the line $AD$ intersect $k$ at $L \neq D$ and denote the excentre of $ABC$ opposite to $A$ by $K$. Let $M$ and $N$ be the midpoints of $BC$ and $KM$ respectively.
Prove that the points $B$, $C$, $N$, and $L$ are concyclic.
Školjka