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

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: .

We can represent the same equation as: .

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

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.  

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

b

step-by-step explanation:

the word superfluous means unnecessary