In triangle ABC, angle A is straight. Prove that line AC touches a circle centered at point B and radius AB.

A straight line that has a single common point with a circle is a tangent, a common point is a tangency point.
It is known that:
AB – perpendicular to the AC (according to the problem statement).
AB is the radius of the circle.
AB with a straight line AC makes a right angle.
Point A is the common point of the circle and AC, since otherwise the circle would have one more radius – longer than AB, and the triangle AB – one more vertex A, which cannot be.