In the triangle $ABC$, let $\ell$ be the bisector of the external angle at $C$. The line through the midpoint $O$ of $AB$ parallel to $\ell$ meets $AC$ at $E$. Determine $|CE|$, if $|AC|=7$ and $|CB|=4$.
Source: Baltic Way 1995
Tags: geometry proposed, geometry
In the triangle $ABC$, let $\ell$ be the bisector of the external angle at $C$. The line through the midpoint $O$ of $AB$ parallel to $\ell$ meets $AC$ at $E$. Determine $|CE|$, if $|AC|=7$ and $|CB|=4$.