Theorem: If a tangent segment and a secant segment are drawn to a circle from an external point, then the square of the length of the tangent equals the product of the length of the secant with the length of its external segment.
In your case this theorem sounds as
[tex]PA^2=PE\cdot PB.[/tex]
If PA=6 and PE=4, then
[tex]6^2=4\cdot PB,\\ \\PB=\dfrac{6^}{4}=\dfrac{36}{4}=9.[/tex]
Note that PB=PE+BE, then
9=4+BE,
BE=9-4=5.
Answer: correct choice is C.
