If a segment is perpendicular to a radius at its endpoint on a circle, then the segment is tangent to the circle. Therefore, to determine whether a tangent is shown on the diagram, it is enough to determine if AB, which appears to be a tangent segment, forms a right angle with the radius of ⊙ C.
Note that the length of the second radius is missing in the graph. Since in any circle the lengths of any radius are constant, the length of the missing radius is 20.
Now, we will use the Converse of the Pythagorean Theorem. We will substitute the given side lengths into the Pythagorean Theorem. If we obtain a true statement, the triangle is a right triangle. If we have a right triangle, AB is a tangent segment. If we do not have a right triangle, the line shown is not a tangent segment.
Since we did not obtain a true statement, the triangle in the diagram is not a right triangle. Therefore, AB does not form a right angle with the radius. By the Tangent Line to Circle Theorem, the segment is not tangent to ⊙ C.
