Question

Find AE, if EB = 16 cm DE = 10 cm and EF = 8 cm.

Answer 1

AE will =8 because EB is twice the length of AE

Answer 2

`AE=5\text{ cm}`

Explanation:

We have been given an image of a circle and we are asked to find the measure of measure of AE.

We will use intersecting chords theorem to solve for AE. Intersecting chords theorem states that the products of the lengths of the line segments on each chord are equal.

Using above theorem we can set an equation as:

`AE\cdot EB=DE\cdot EF`

Upon substituting our given values in above equation we will get,

`AE\cdot 16=10\cdot 8`

Upon dividing both sides of our equation by 16 we will get,

`(AE\cdot 16)/(16)=(10\cdot 8)/(16)`

`AE=(10\cdot 1)/(2)`

`AE=5`

Therefore, the measure of AE is 5 cm.