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Given the following information, what is the position of the other vertex of the great circle between A and B?

Point A: 50°N, 070°W
Point B: 50°N, 080°W
Position of one of the vertices of the great circle between A and B: 50°06.4’N, 075°00.0’W

  • A
    00°00.0’N, 105°00.0’E
  • B
    00°00.0’N, 075°00.0’W
  • C
    50°06.4’S, 075°00.0’W
  • D
    50°06.4’S, 105°00.0’E

Refer to figure.
The vertex of a great circle is the point where the great circle reaches the highest latitude, that is, the farthest possible distance from the equator. A great circle has two opposite vertices in the Northern and Southern Hemisphere, and these are at the same latitude.

The given vortex is at latitude 50º06.4'N. Therefore, the other vertex must be at the same latitude in the opposite hemisphere: 50º06.4'S.

Now, the two vertices are also 180º of longitude apart. The given vertex is at longitude 075°00.0’W. Therefore, the other vertex must be at longitude: 180°00.0’ - 075°00.0’E = 105°00.0’E.

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