The bisector of the angle $A$ of the triangle $ABC$ intersects the side $BC$ at $D$. A circle $c$ through the vertex $A$ touches the side $BC$ at $D$. Prove that the circumcircle of the triangle $ABC$ touches the circle $c$ at $A$.
Source:
Tags: geometry, angle bisector, tangent circles
The bisector of the angle $A$ of the triangle $ABC$ intersects the side $BC$ at $D$. A circle $c$ through the vertex $A$ touches the side $BC$ at $D$. Prove that the circumcircle of the triangle $ABC$ touches the circle $c$ at $A$.