1. ## Question about angle and segment relationships?

Heres the question: Secants $ABC$ and $ADE$ intersect at point $A$ outside the circle. If $AC=20, AB=5, AD=4$, find $AE$.

Okay so i did
$20*5=4*x$
$100=4x$
$100/4=4x/4$
$x=25$

Okay so my question is, is the answer $25$ or do i subtract $4$ from it?

2. AE is 25. AE (or ADE) is comprised of AD and DE. You found AE (which was asked). AD = 4 and DE = 21.

Good!

3. Originally Posted by eh501
Heres the question: Secants $ABC$ and $ADE$ intersect at point $A$ outside the circle. If $AC=20, AB=5, AD=4$, find $AE$.

Okay so i did
$20*5=4*x$
$100=4x$
$100/4=4x/4$
$x=25$

Okay so my question is, is the answer $25$ or do i subtract $4$ from it?
Actually, the correct set up is this: If two secants intersect at an external point, the product of the external segment of one secant times the whole secant is equal to the external part of the other secant times the whole secant.

In other words, by my diagram: $AB \cdot AC=AD \cdot AE$

Therefore,

$5\cdot20=4\cdot(4+DE)$

$AE=4+DE$

$5\cdot20=4(4+DE)$

$100=16+4(DE)$

$84=4(DE)$

$21=DE$

$AE=4+DE \Longrightarrow 4+21=25$