Problem

Source: Switzerland - Swiss MO 2012 p6

Tags: geometry, circumcircle, equal circles, parallelogram



Let $ABCD$ be a parallelogram with at least an angle not equal to $90^o$ and $k$ the circumcircle of the triangle $ABC$. Let $E$ be the diametrically opposite point of $B$. Show that the circumcircle of the triangle $ADE$ and $k$ have the same radius.