Question 116
Let $ABC$ be a triangle with $m(\widehat{BAC}) = 60^{\circ}$. Let $D$ and $E$ be the feet of the perpendiculars from $A$ to the external angle bisectors of $\widehat{ABC}$ and $\widehat{ACB}$, respectively. Let $O$ be the circumcenter of the triangle $ABC$. Prove that the circumcircles of the triangles $ADE$ and $BOC$ are tangent to each other.
