In the diagram, two tangents drawn from an external point B meet the circle at D and C. Click and drag any of the blue points to change the shape and orientation of the diagram. What do you observe?

Consider the triangles OCB and ODB.

- Why is OC = OD?
- Why is <OCB = <ODB?
- Given that OB is common, what test could be used to prove that triangles OCB and ODB are congruent?
- What does the result in (3) tell us about BC and BD? Why is this so?