Question

In circle O, chord AB is 9 inches from the center. The diameter of the circle exceeds the length of AB by 2 inches. Find the length of AB

Answer 1

let the chord AB = 2x
then the diameter = 2x+2
or the radius = x+1

This allows me to draw a right-angled triangle with sides x and 9 and hypotenuse x+1
(x+1)^2 = x^2 + 9^2
x^2 + 2x + 1 = x^2 + 81
2x = 80
x = 40

AB = 80

check:
diameter = 82

is 41^2 = 40^2 + 9^2 ?
LS = 1681
RS = 1600+81
= 1681
= LS

YES