document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #709825 by greenestamps(13200) $\"\"$ $\"About$

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Draw a 2-dimensional picture of the situation.
\n" ); document.write( "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.
\n" ); document.write( "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.

\n" ); document.write( "So you will know the radius of the circle if you can use the given information to find the length of AB.

\n" ); document.write( "And you do have enough information to do that.

\n" ); document.write( "There is a theorem from geometry that says
\n" ); document.write( " $\"%28CD%29%5E2+=+%28CB%29%28CA%29\"$

\n" ); document.write( "So if the radius is x (so that the diameter is 2x),
\n" ); document.write( " $\"16%5E2+=++8%282x%2B8%29\"$
\n" ); document.write( " $\"256+=+16x%2B64\"$
\n" ); document.write( " $\"192+=+16x\"$
\n" ); document.write( " $\"x+=+12\"$

\n" ); document.write( "The radius of the circle is 12 feet. \n" ); document.write( "

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