# Tangents from External Point

- Author:
- Callum Marshall, Joe Chung

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?