Tangents from External Point
If two tangents are drawn from an external point to a circle then the lengths of the tangents are equal. Drag point A to see the theorem in action.
Question 1
UNCHECK the first box to remove the lengths of AC and AB. If you now had to PROVE they were equal, WITHOUT checking the Step 1 box, what do YOU think should be the FIRST STEP...?
Question 2
Check off STEP 1 - were you correct? WITHOUT 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? Hint: What information do you need to prove that two right-angled triangles are congruent?
Question 4
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. Is it obvious why?