Answer: The correct option is second. The length of line segment PQ is 5 units.
Explanation:
From the given figure it is noticed that the MN is the tangent to the circle at point M and its length is 6.
The line PQ is the secant line with length x and QN is external secant segment with length 4 .
According to the tangent secant theorem the square of tangent is equal to the product of external secant with the sum of the of secant and external secant.
[tex]MN^2=QN\times PN[/tex]
[tex]6^2=4\times (x+4)[/tex]
[tex]36=4x+16[/tex]
[tex]20=4x[/tex]
[tex]x=5[/tex]
Therefore, the length of line segment PQ is 5 units.
