In a triangle ABC AB = 4 cm, BC = 3 cm, AC = 5 cm. Prove that an AB-segment is a tangent

In a triangle ABC AB = 4 cm, BC = 3 cm, AC = 5 cm. Prove that an AB-segment is a tangent line drawn from point A to a circle with center at point C and radius 3 cm.

In the triangle ABC, the Pythagorean theorem is fulfilled.

5 ^ 2 = 25.

3 ^ 2 + 4 ^ 2 = 9 + 16 = 25.

Then triangle ABC is rectangular, angle CBA = 90.

Since the vertex C of the triangle is the center of the circle, and the radius of the circle is equal to the length of the leg BC, BC is the radius of the circle.

The radius of BC is perpendicular to AB, then point B is the point of tangency, and AB is tangent to the circle, which was required to prove.