How to prove a line is NOT a tangent to a circle

Question

A line is given as AB. It is required to prove that it is not a tangent to a circle given as OEB

Answer 1

Assuming O is the centre of the circle and B is a point on the circumference, the angle ABO is a right angle if and only if AB is a tangent. So, if AB is not perpendicular to BO, AB is not a tangent.

In the picture the red line AB is a tangent, and touches the circle at one point B only. The blue line AB is not a tangent and intersects the circle at two points, B and E.