Explanation:
1.
the indicated point in the middle is the center point of the circle.
the line perpendicular to a chord going through that center solid the chord in half.
so,
x = 9
2.
Pythagoras
c² = a² + b²
13.5² = x² + 10.4²
182.25 = x² + 108.16
x² = 74.09
x = 8.607554821...
3.
Intersecting Chords Theorem
(part one of chord 1)×(part two of chord 1) =
= (part one of chord 2)×(part two of chord 2)
6x = 10×9 = 90
x = 90/6 = 30/2 = 15
4.
Intersecting Chords Theorem again
x(x+3) = 4×10 = 40
x² + 3x = 40
x² + 3x - 40 = 0
generation solution to a quadratic equation
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
a = 1
b = 3
c = -40
x = (-3 ± sqrt(3² - 4×1×-40))/(2×1) =
= (-3 ± sqrt(9 + 160))/2 = (-3 ± sqrt(169))/2 =
= (-3 ± 13)/2
x1 = (-3 + 13)/2 = 10/2 = 5
x2 = (-3 - 13)/2 = -16/2 = -8
negative values for a length do not make sense, so x = 5 is our solution
5.
Intersecting Chords Theorem
(x+1)×4 = (x-1)×5
4x + 4 = 5x - 5
9 = x