SOLUTION: A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?
Question 1210153: A and B are two points on a sphere of radius 2. We know the space distance between A and B is 2, What is distance from A to B along the (minor) arc of a great circle?
The triangle is equilateral, so the central angle is 60o,
so the arc is of the circumference of a great circle.
The circumference of a great circle is
The length of the arc is or .
Edwin
If O is the center of the sphere, then OA, OB and AB all have length 2, so triangle AOB is equilateral; its angles are each 60 degrees.
The angle subtended by minor arc AB is then 60 degrees, which is 1/6 of a circle. The length of minor arc AB is then 1/6 of the circumference of a circle with radius 2.