Suppose that
is a cyclic quadrilateral and
. Points
and
belong to the segments
and
respectively, and
. Segments
and
are height and median of triangle
, respectively.
is the point symmetric to
with respect to
. Prove that the lines
and
are parallel.
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Suppose that $ABCD$ is a cyclic quadrilateral and $CD=DA$. Points $E$ and $F$ belong to the segments $AB$ and $BC$ respectively, and $\angle ADC=2\angle EDF$. Segments $DK$ and $DM$ are height and median of triangle $DEF$, respectively. $L$ is the point symmetric to $K$ with respect to $M$. Prove that the lines $DM$ and $BL$ are parallel.
Školjka