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Tangents to a circle from an external point

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.

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