Answer to Question #30702 in Geometry for Nevila

Question

I know that the largest circle on the sphere is the great circle. But in my problem, we are working on the circles that have the center on the surface of the sphere. Question is: 1. In a sphere with radius 1000, compare the area of the circle with radius 500 and the area with radius 1500 (Hint: consider a point; ex. North pole as center for both circles). This has to be done roghly without calculating the areas. 2. What is the area contained by the largest circle that can be drawn on the surface of this sphere (center on the north pole)? 3. what is the circumference of the circlecontaining this largest area? Any help is appreciated. Thanks