Question

Segments PD and PE have a Common Point at P. According to the diagram which pair of numbers could represent the lengths of segments PC and CE

A)PC=6 and CE=4
B)PC=6 and CE=6
C)PC=5 and CE=6
D)PC=6.5 and CE=5.5

Answer 1

The answer would be A since 5 times 12 equals 60 and the other pair could be 10 times 60 so pc equals 6 and ce equals 4

Answer 2

A)PC=6 and CE=4

Step-by-step explanation:

We have been given that segments PD and PE have a Common Point at P.

Since the intersecting secants theorem states that if two secant segments are drawn to a circle from an external point, then product of one secant segment and its external segment is equal to the product of other secant and its external segment.

Using intersecting secants theorem we can can write an equation as:
`(PD) \cdot PB=(PE)\cdot PC`.

We can represent the same equation as:
`(PB+BD) \cdot PB=(PC+CE)\cdot PC`.

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

`(5+7) \cdot 5=(PC+CE)\cdot PC`

`(12) \cdot 5=(PC+CE)\cdot PC`

`60=(PC+CE)\cdot PC`

Upon looking at our given choices we can see that lengths provided in option A meet our criteria.

Let us check our answer by substituting the lengths provided in option A in above equation.

`60=(6+4)\cdot 6`

`60=10\cdot 6`

`60=60`

Therefore, the pair of numbers provided by option A can represent the lengths of segments PC and CE.