Consider five points
,
,
,
and
such that
is a parallelogram and
is a cyclic quadrilateral. Let
be a line passing through
. Suppose that
intersects the interior of the segment
at
and intersects line
at
. Suppose also that
. Prove that
is the bisector of angle
.
Author: Charles Leytem, Luxembourg
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Consider five points $A$, $B$, $C$, $D$ and $E$ such that $ABCD$ is a parallelogram and $BCED$ is a cyclic quadrilateral. Let $\ell$ be a line passing through $A$. Suppose that $\ell$ intersects the interior of the segment $DC$ at $F$ and intersects line $BC$ at $G$. Suppose also that $EF = EG = EC$. Prove that $\ell$ is the bisector of angle $DAB$.
Author: Charles Leytem, Luxembourg
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