Geometry

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

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  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

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