SOLUTION: A large industrial winch is enclosed. There are 15 inches of the cable hanging free off of the winch's spool and the distance from the end of the cable to the spool is 8 inches. Wh
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Question 1179961: A large industrial winch is enclosed. There are 15 inches of the cable hanging free off of the winch's spool and the distance from the end of the cable to the spool is 8 inches. What is the diameter of the spool? Answer by greenestamps(13200) (Show Source):
The description is of a circle (the spool) with a tangent of length 15 (the free cable) and a secant of length 8+d, where the 8 is the distance from the end of the rope to the spool and d is the diameter of the spool. The operative geometric fact is this:
The square of the length of a tangent to a circle is equal to the product of the length of the whole secant and the length of the portion of the secant external to the circle.
That gives you an equation that is easily solved to find the diameter d of the spool:
I leave it to you to do the simple algebra to find the answer.
