Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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1
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4answers
862 views

Unit circle metric

Let $S^1$ the unit circle in $\mathbb{R}^2$ and $$d: S^1\times S^1\to\mathbb{R}$$ $$d(\theta_1,\theta_2) = \left\{ \begin{array}{ll} |\theta_1-\theta_2| & \mbox{if } ...
55
votes
4answers
6k views

Why is a circle in a plane surrounded by 6 other circles

When you draw a circle in a plane you can perfectly surround it with 6 other circles of the same radius. This works for any radius. What's the significance of 6? Why not some other number? I'm ...
4
votes
2answers
2k views

Calculating a tangent arc between two points on two circles

How can I calculate the arc between two circles? The arc must be tangent to the two points on the circles. Here is a picture illustrating it. I'm trying to code and calculate the orange arc and the ...
2
votes
1answer
1k views

How to find a (longitude, latitude) point on a circle when given only the center (longitude, latitude) point and radius measured in Feet

How do I find a (longitude, latitude) point (any will do) on a circle where the only info I have is a (longitude, latitude) center point, and a radius measured in Feet (ft.)?
3
votes
1answer
880 views

Find the radius of a circle based off of its intersection with another

So I have some circles that look kinda like this: I'm given the radius of the circle with center point A which is also the distance AB, the distance AB between the two center points on the x axis ...
6
votes
3answers
13k views

Proof of Angle in a Semi-Circle is 90 degrees

There is a well known theorem often stated as the angle in a semi-circle being 90 degrees. To be more accurate, any triangle with one of its sides being a diameter and all vertices on the circle has ...