Which of the following pairs of longitudes forms a Great Circle?

Answer Details

A great circle is a circle on the Earth's surface that has the same diameter as the Earth. It is the largest possible circle that can be drawn on a sphere. Any two points on a great circle are the same distance from each other, and the shortest distance between any two points on a sphere always lies along a great circle.
To determine which of the given pairs of longitudes forms a Great Circle, we need to find the midpoint between the two longitudes and then draw a circle with that midpoint as its center and the radius equal to the radius of the Earth.
So, for each pair of longitudes, we calculate the average of the two values and check if the resulting line passes through the center of the Earth. The pair of longitudes that passes through the center of the Earth is the one that forms a Great Circle.
Calculating the midpoint of the given pairs of longitudes, we get:
- 60°E and 140°E: Midpoint = (60 + 140)/2 = 100°E
- 40°W and 140°E: Midpoint = (360-40 + 140)/2 = 230°E
- 20°W and 160°W: Midpoint = (360-20 + 360-160)/2 = 140°W
- 10°E and 180°: Midpoint = (10 + 180)/2 = 95°E
Since only the pair of longitudes 40°W and 140°E passes through the center of the Earth, it forms a Great Circle.