Consider five points
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
,
![B](/media/m/c/e/e/ceebc05be717fa6aab8e71b02fe3e4e3.png)
,
![C](/media/m/5/a/b/5ab88f3f735b691e133767fe7ea0483c.png)
,
![D](/media/m/7/0/0/7006c4b57335ab717f8f20960577a9ef.png)
and
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
such that
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
is a parallelogram and
![BCED](/media/m/d/6/b/d6be5c70d91a01b6384af5467ef0d7d5.png)
is a cyclic quadrilateral. Let
![\ell](/media/m/b/4/6/b4635d1d170e32cfdfdade69153682f8.png)
be a line passing through
![A](/media/m/5/a/e/5ae81275ee67d638485e903bdc0e9cde.png)
. Suppose that
![\ell](/media/m/b/4/6/b4635d1d170e32cfdfdade69153682f8.png)
intersects the interior of the segment
![DC](/media/m/3/4/d/34d909d24fdb3a0dd783c13a369556ce.png)
at
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
and intersects line
![BC](/media/m/5/0/0/5005d4d5eac1b420fbabb76c83fc63ad.png)
at
![G](/media/m/f/e/b/feb7f8fc95cee3c3a479382202e06a86.png)
. Suppose also that
![EF = EG = EC](/media/m/8/7/f/87f6651216c630167221f331b84ce402.png)
. Prove that
![\ell](/media/m/b/4/6/b4635d1d170e32cfdfdade69153682f8.png)
is the bisector of angle
![DAB](/media/m/b/2/4/b2422dad253279a85572e4d78eb1a6d1.png)
.
Author: Charles Leytem, Luxembourg
%V0
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