Question 1095262
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Radius to the tangent point and the tangent line are perpendicular.


So, the triangle formed by these three lines

    - Radius to the tangent point;
    - tangent line,  and
    - the line connecting you with the center of the silo

is an right-angled triangle.


Apply the Pythagorean theorem

    (R+8)^2 = R^2 + 16^2,

     R^2 + 16R + 64 = R^2 + 256  ====>  16R = 256-64 = 192  ====>  R = {{{192/16}}} = 12.


<U>Answer</U>.  R = 12 feet.
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