Question

L is a point of tangency. Segments PL and PN have a common point at P. Find the length KN.

Answer 1

Answer is 4.5.

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Answer 2

In the attached file, you will see the circle for this problem.
The given is PL = 10 whereas PK = 8
To answer the problem:
PK * PN = PL^2
Let PN = x
8x = 10^2

8x = 100

x = 100/8

x = 12.5
KN = PN - PK

12.5 - 8 = 4.5 would be the length of segment KN.