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

August 28, 2021 | education

| 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.

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