Reflections in Angle bisector

Question

In a triangle $ABC$, take the tangent to the circumcircle of $ABC$ at $A$. Reflect this line through the angle bisector at $A$. prove that this reflected line is parallel to $BC$.

I'm looking for a quick and simple proof of this fact.

Answer 1

The tangent is anti paralel to $BC$ since its angles are oposite to the triangle $ABC$, because the semi inscribed angles. A reflexion to the angle bisector inverses the angles,so that the angles corresponds to the triangle's direction.