Answer:
According to the theorem of chords intersecting inside the circle,
1) 15 * 8 = 10 * x
120 = 10x
120/10 = x
12 = x
2) 21 * 10 = 14 * x
210 = 14 x
210/14 = x
15 = x
3)10 * 4 = 5x
40 = 5x
40/5 = x
8 = x
4) 5x * 2x = 10*9
10x^2 = 90
x^2 = 90/10
x^2 = 9
x = √9
x = 3
5)3x + 3 * 3x = 10 * 18
9 x^2 + 9x = 180
dividing the whole eq. by 9
x^2 + x = 20
x^2 + x - 20 = 0
x^2 + 5x - 4x - 20 = 0
x(x + 5) - 4(x + 5) = 0
x - 4 = 0 OR x + 5 = 0
x = 4 or x = -5
The length cannot be negative, so,
x = 4
