Tangents from External Point

[size=150]If two tangents are drawn from an external point to a circle then the lengths of the tangents are equal. [b]Drag point A to see the theorem in action.[/b][br][/size]
Question 1
UNCHECK the first box to remove the lengths of AC and AB. [br][br]If you now had to PROVE they were equal, [b]WITHOUT [/b]checking the Step 1 box, what do YOU think should be the FIRST STEP...?
Question 2
Check off STEP 1 - were you correct?[br][br][b]WITHOUT[/b] checking off the What I Know box, write down what you now know that will be helpful.
Question 3
Click on Step 2 - you now have all you need to prove that AC = BC. How do you do that?[br][br]Hint: What information do you need to prove that two right-angled triangles are congruent?
Question 4
[size=150][size=100]The line joining the external point and the centre of the circle bisects the angle between the tangents. Check the box to see the angles.[br][br]Is it obvious why?[/size][/size]
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Information: Tangents from External Point