A mobile, on the surface of the earth, is at a point A. Travels 200 km south arriving at a point B. Later moves 200 km west arriving at a point C. Finally moves over 200 kilometers to the north, back to point A. Assuming that the surface of the earth is a perfect sphere, which the geometric place of the points where the mobile could be?
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The point $A$ is the north pole. – Daniel Robert-Nicoud Oct 04 '13 at 22:05
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@DanielRobert-Nicoud: Not necessarily. There is a double infinity of points that qualify. – André Nicolas Oct 04 '13 at 22:10
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@AndréNicolas Not if you want to travel exactly west from $B$ to $C$. – Daniel Robert-Nicoud Oct 04 '13 at 22:16
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1@DanielRobert-Nicoud: yes, the rest are near the South pole – Ross Millikan Oct 04 '13 at 22:21
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@RossMillikan Ah, you're right. I hadn't considered those points... – Daniel Robert-Nicoud Oct 04 '13 at 22:25
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Just so we have an answer, one possibility is the North pole. There are more near the South pole, where the Westward trip circles the pole any whole number of times.
Ross Millikan
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Yes, very good, The North Pole and even a multitude of circles, all nearby south pole, whose length is 200km, 100km, 50km, 25km, ... – Jorge Augusto Oct 04 '13 at 23:28
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Well, actually 200km north of those circles, all nearby south pole, whose length is 200km, 100km, 50km, 25km, ... – peterwhy Oct 04 '13 at 23:56