Question 44
In $\triangle ABC$, let $D$ be the point on side $BC$ such that $AB + BD = DC + CA$. The line $AD$ intersects the circumcircle of $\triangle ABC$ again at point $X \neq A$. Prove that one of the common tangents of the circumcircles of $\triangle BDX$ and $\triangle CDX$ is parallel to $BC$.