[color=#000000]In the applet below, two secant segments are drawn to a circle from a [/color][color=#1e84cc]point outside the circle[/color][color=#000000]. [br]Interact with the applet below for a few minutes, then answer the questions that follow. [/color]

[color=#000000][b]Questions: [/b] [br][br]1) What can you conclude about the measure of the [/color][color=#ff00ff]pink angles[/color][color=#000000]? [br][br]2) Why can you conclude this? [br] (If you need a hint, see the worksheet found here: https://tube.geogebra.org/m/dzksdCfS)[br][br]3) Note that the [/color][color=#1e84cc]blue angle[/color][color=#000000] is congruent to itself. What property justifies this? [br][br]4) Move the slider all the way to the end one more time. [br] What can you conclude about triangle [i]ABC[/i] and triangle [i]DEC[/i]? [br] What previously learned theorem justifies this fact? [br][br]5) Use your result from (4) to write a relationship (i.e. equation) among the lengths [/color][color=#980000]a[/color][color=#000000], [/color][color=#980000]b[/color][color=#000000], [/color][color=#38761d]ext_a[/color][color=#000000], and [/color][color=#38761d]ext_b[/color][color=#000000]. [br][br]6) Rewrite the equation you wrote in (5) above so that each side of the equation is written as a product. [br][br]7) Now, reset the slider again. [br] Then, drag point [i]A[/i] upwards along the circle so that it lies right on top of point [i]E[/i]. [br] ([i]This now causes the secant segment to turn into a tangent segment.)[br] [/i]Reslide the slider again one more time. [br] What can you conclude about the lengths [/color][color=#980000]a[/color][color=#000000] and [/color][color=#38761d]ext_a[/color][color=#000000] in this special scenario? [br][br]8) Answer questions (4) - (5) again within this context. [br][/color]