math

ABCDE is a circle with centre O. The diameter, AC, is extended to the point F so that CF = 16 cm. The line BF is the tangent to the circle at B and FDE is a straight line such that FD = 18 cm and chord DE = 14 cm (D and E are points of intersection of the line and the circle). Find the radius of the circle.

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  1. This looks like an application of the tangent-secant theorem
    If the radius is r
    Using the secant FE
    BF^2 = FE*FD = 32*18 = 576
    Using the secant FA
    BF^2 = 16(2r+16)

    16(2r+16) = 576

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