Lines UW and VT are intersecting chords at point K. According to the intersecting chords theorem,
VK * KT = UK * KW
From the diagram,
VK = x + 4
KT = x - 1
UK = 6
KW = 6
Thus,
(x + 4)(x - 1) = 6 * 6
x^2 - x + 4x - 4 = 36
x^2 + 3x - 4 - 36 = 0
x^2 + 3x - 40 = 0
We would solve the quadratic equation by factorisation. We would two terms such that their sum or difference is 3x and their product is - 40x^2. The terms are 8x and - 5x. Thus, we have
x^2 + 8x - 5x - 40 = 0
x(x + 8) - 5(x + 8) = 0
(x + 8) = 0 and (x - 5) = 0
x = - 8 and x = 5
The value for x can only be positive. Thus,
KT = x - 1 = 5 - 1
KT = 4
The correct option is B