Question 818193: I am not a student, and this is not a homework question, but I am hoping that you can help me solve this puzzle that occurred to me while looking at a fan belt in my car, and I thought it was mathematically interesting.
You have two circles. The radius of the first circle is 200mm. The radius of the second circle is 125mm. The center points of the circles are 305mm apart, and the center point of the large circle is directly vertical to the center point of the small circle. Tangent segments extend from the outer edges of the large circle to the outer edges of the small circle (that is to say, the segments do not cross). What is the perimeter of the shape formed by the two circles and the two tangent lines? (In more common terms... how long does a fan belt around two wheels need to be?)
If the circles were the same exact size, this would be an easy question, but I was not able to figure out some aspects of the information needed to complete the solution.
If either of the circles were to change, even slightly, then the chords of both the large and small circle at the points where the tangent segments touch the circle would also change. This, in turn, would change how much of the circumference of the circle should be included in the calculation of the total perimeter.
What I was able to figure out was that the perimeter of the shape (my wife referred to it as an "obloid" which made me laugh) would be something like this:
The circumference of the large circle minus the arc between the two points where the tangent segments meet the large circle
PLUS
the circumference of the small circle minus the arc between the two points where the tangent segments meet the small circle
PLUS
the length of both tangent segments (or twice the length of a single tangent segment).
I am very curious to know how this problem could be solved, and would love to hear from you! As I mentioned, this is not a "real" problem or a homework problem, so I also understand if this isn't quite what you do. I just thought it was an interesting puzzle, and thought you might agree!
Thanks in advance for reading, considering, and thinking!
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! take half the circumference (pi*r )of each pi*200 +pi*125 of the two circles plus twice the distance to the centers (2*305)
the tangent segments should be the same length as from center to center.
pi*200 +pi*125 +(2*305)
|
|
|
