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what is the length of ?

10.5
4
10
6

OK.  Take it slow and easy, one step at a time.

-- Draw a line from the center of the circle to the left end of the
horizontal chord.
(That point doesn't have an identification letter, but it's the other
end of the '10' from point 'A'.)

-- Since that line is also a radius of the circle, its length is 14.5 .

-- When you drew the line, you made a right triangle inside the circle. 
The line you drew is the hypotenuse of the right triangle.

-- You know the length of the hypotenuse (14.5), and you know
the length of one leg (10).  So you can calculate the length of the
other leg ... from the center to point 'A'.  That leg is √(14.5² - 10²)

-- Now you know the distance from the center of the circle to point 'A'.
The length of AB is (the radius) minus (the leg that you just found).

Seem reasonable ?

I got 4 for AB.  But I was working fast and sloppy.  You need to check it.

(1/x + 1)^2 + 6 (1/x + 1) +5

If you divide 0.1 and 0.6 you wii get 0.166666 which rounds to .167 which is answer b