In the diagram, the tangent to the circle with centre O touches the circle at the point C. Click and drag any of the blue points to change the size and orientation of the diagram. What observations can you make regarding the angle between the tangent and the radius at the point of contact?
The shortest distance from a point to a line is the perpendicular distance. Consider the distance OB, for example. Clearly, OC < OB (for any position of B, other than C). What does this tell us about the distance OC? What does this tell us about <OCB?