Question

If PA=6, PD=4, and BE=5, find PE
4
5
6

Answer 1

its 4

Step-by-step explanation:

Answer 2

Option A: 4 is the length of PE

Step-by-step explanation:

Given that PA=6, PD=4, and BE=5

We need to determine the length of PE

The length of PE can be determined using the intersecting secant tangent theorem.

Applying the secant tangent theorem, we get,

`PA^2=(BE+PE)(PE)`

Substituting the values of the PA and BE, we get,

`6^2=(5+PE)(PE)`

Simplifying, we get,

`36=5PE+PE^2`

Subtracting both sides of the equation by 36, we get,

`0=-36+5PE+PE^2`

Switch sides, we get,

`PE^2+5PE-36=0`

Solving this equation, we get,

`(PE+9)(PE-4)=0`

Equating each term equal to zero, we get,

`PE+9=0` and
`PE-4=0`

Simplifying, we get,

`PE=-9` and
`PE=4`

The value of PE cannot be negative.

Thus, the length of PE is 4.

Hence, Option A is the correct answer.