# Finding arbitrary circumference/circle on a sphere

1. Nov 2, 2011

### Hyperian

I need to find the green circle described in the picture below. (go from top left to bottom right)

The base values are:
the radius of the ball = d1 = 10
height down into the ball that forms the circle d2. h = 0.5.
I don't know if these values are useful in the end, but R on the right is sqrt(19)/2. which is the radius of the smaller circle, and also how far this circle is from the top. a way to visualize that is this picture.
[URL]http://upload.wikimedia.org/wikipedia/commons/5/56/Small_circle.svg[/URL]
from the formation of the equilateral triangle, a 90 degree angle is made, which finally forms a line that travels from that point of the ball to the bottom point of the ball, and finally back to where it is from.

so in the end, i am looking for the circumference of the green line on the ball. This was very hard to describe to, even to professors, which in the end couldn't help me, so I thought i would ALSO make a video of the problem!
http://www.youtube.com/watch?v=fCHQLQiLYUU"
The L in the video is wrong, it should be R, which would describe the same R as in the diagram!
Feel free to ask for more details, since even i don't think there might be enough information initially to figure this one out.

If you guys figure it out, i'll explain what this is used for! it's not just a purely mathematical exercise!

Last edited by a moderator: Apr 26, 2017
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Can you offer guidance or do you also need help?