Question

In the diagram below of circle O, chords AB and CD intersect at E. If AE = 6, BE = 4, and

DE= 3, what is the length of CE?*

Answer 1

Answer: 8

Explanation:

I recently had the exact same question on an exam, so I am assuming you have the same numbers.

AE = 6

BE = 4

DE = 3

To start, label the diagram appropriately.

As for CE, you need to put a variable, let's say x, since you don't now the number.

Next, apply the circle rule that states the necessary formula for this problem.

Since there are two lines stretching from one end to the next of the circle, you multiply one number from the opposite.

AE = 6 and BE = 4, so multiplying the two gets you 24.

This means that DE multiplied by x is also 24.

If DE = 3, divide 24 / 3 to isolate the variable.

Once you do this, you get 8 on one side, and x on the other. X, or CE, is 8.