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G.GCI.2 Tangents

In the applet below, 2 tangent rays are drawn to a circle from a point outside that circle. Interact with the applet below for a few minutes, then answer the questions that follow.
Questions: 1) How would you describe the intersection of a radius drawn to either point of tangency? 2) What can you conclude about the lengths EB and EA? 3) How could you have proven your response to question (2) true WITHOUT seeing the rotation of the pink segment in the applet above? (Hint: Look at the triangles!) 4) Write a proof that shows your response to (2) is true. You may assume that your response to (1) holds true as you write this proof.