Let $ABC$ be a triangle with $AB=AC$, and let $M$ be the midpoint of $BC$. Let $P$ be a point such that $PB<PC$ and $PA$ is parallel to $BC$. Let $X$ and $Y$ be points on the lines $PB$ and $PC$, respectively, so that $B$ lies on the segment $PX$, $C$ lies on the segment $PY$, and $\angle PXM=\angle PYM$. Prove that the quadrilateral $APXY$ is cyclic.
Školjka 
be a triangle with 
, and let 
be the midpoint of 
. Let 
be a point such that 
and 
is parallel to 
and 
be points on the lines 
and 
, respectively, so that 
lies on the segment 
, 
lies on the segment 
, and 
. Prove that the quadrilateral 
is cyclic.