Question 172
Triangle $ABC$ is obtuse with $\angle ABC \gt 90^\circ$. Let $\ell$ be the external bisector of $\angle BCA$, and let $AB$ (extended) meet $\ell$ at $D$. The circumcircle $\Gamma$ of triangle $BCD$ has centre $O$. Let $E$ be the point where the line through $A$ perpendicular to $DO$ meets $\ell$. Prove that $BE$ is tangent to the circle $\Gamma$.