SOLUTION: you are standing at c. 8 feet from a silo. A is the center of the circular base of the silo. the distance to point of tangency is 16 feet What is the radius of the silo

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Question 1095262: you are standing at c. 8 feet from a silo. A is the center of the circular base of the silo. the distance to point of tangency is 16 feet What is the radius of the silo
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Draw a 2-dimensional picture of the situation.
From where you are standing at C, it is 16 feet to the point D on the "edge" of the silo (circle) as you see it.
When it says you are 8 feet from the silo, it means that 8 feet is the shortest distance from C to any point on the silo (circle). Let B be that point on the circle that you are closest to. The line from where you are to that point B on the circle, extended through the circle to the other side of the circle at A, will pass through the center of the circle. That means AB is a diameter of the circle, which is of course twice the radius.

So you will know the radius of the circle if you can use the given information to find the length of AB.

And you do have enough information to do that.

There is a theorem from geometry that says


So if the radius is x (so that the diameter is 2x),





The radius of the circle is 12 feet.
Answer by ikleyn(52781)   (Show Source): You can put this solution on YOUR website!
.
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 =  = 12.


Answer.  R = 12 feet.


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