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

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5
votes
2answers
659 views

Finding point on a circle

I know how to find a point on a circle given a radius and an angle, but my knowledge of trigonometry doesn't extend much further than that. My question is probably best explained diagrammatically: ...
0
votes
1answer
91 views

What's the name of a part of a circle that's formed by an arbitrary intersecting line?

The curved line is a part of a circle with a center at the lower right corner. What would be the name of the shaded region? Thanks
2
votes
1answer
299 views

Getting a Circular Crown's area and perimeter

Okay, this is really bugging me: My Math book has this practice where I need to get the area and perimeter of the next Circular Crown: $R = 3$cm , $r = 1.75$cm. Well, I do it. But my results ...
5
votes
4answers
1k views

Calculate $\pi$ precisely using integrals?

This is probably a very stupid question, but I just learned about integrals so I was wondering what happens if we calculate the integral of $\sqrt{1 - x^2}$ from $-1$ to $1$. We would get the surface ...
3
votes
1answer
186 views

Maximum gap among N points on a circle

If $N$ points on the circumference of a circle are chosen at random, what is the probability $F(\theta)$ that the maximum gap between neighboring points is at least $\theta$? Because the gaps sum to ...
2
votes
1answer
580 views

the equation of a circle on sphere?

one sphere with radius R,named big sphere,two point on it:a(longitude_a,latitue_a),b(longitude_b,latitude_b), dist(a,b)=r, a as center,r as radius,there is another sphere,named little sphere, now what ...
5
votes
2answers
301 views

name of a shape

Let P be a point, not the center, in the interior of a (round) disk D⊂ℝ² and let A and B be points on ∂D such that the line segments AP and BP have equal length. Choose an arc AB. What's the shape ...
6
votes
2answers
2k views

Prove that three points are enough to draw/define one and only one circle

Prove that three points are enough to draw/define one and only one circle, how would this be done?
2
votes
2answers
3k views

Find Coordinates of Touching Point of a Tangent on a Circle

I have a point 'a' with known coordinates, from which I have drawn a tangent to a circle with centre 'c' which is also known. What is the best way of finding the coordinates of point 'b', the touching ...
6
votes
2answers
333 views

Two points on circle resulting in 5 equal regions

What values of $Z_1$ and $Z_2$ make the five regions of the unit circle, shown below, equal in area? $\overline{Z_1}$ and $\overline{Z_2}$ are conjugates of $Z_1$ and $Z_2$; in other words they lie ...
5
votes
3answers
2k views

How many right angled triangles can a circle have?

Here's what I recall of the question from CNML Grade 11, 2010/2011 Contest #3, Question 7: There are 2010 points on a circle, evenly spaced. Ford Prefect will* randomly choose three points on ...
5
votes
3answers
996 views

How to determine arc measures from angles between secant and tangents (without trigonometry)

Given a circle, a point $H$ outside the circle, segments $\overline{HE}$ and $\overline{HT}$ tangent to the circle at $E$ and $T$, respectively, and points $I$ and $G$ on the circle such that $I$, ...
26
votes
3answers
2k views

Have I made a straight line, or a circle?

(Disclaimer: I'm an engineer) Hi everybody, I found this “riddle” posted on the internet: It's meant as a joke, but I do think it deserves an answer :) A bit of background: the orange and blue ...
7
votes
2answers
2k views

Numbers of circles around a circle

"When you draw a circle in a plane of radius 1 you can perfectly surround it with 6 other circles of the same radius." BUT when you draw a circle in a plane of radius 1 and try to perfectly surround ...
1
vote
4answers
827 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 } ...
54
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.)?
2
votes
1answer
841 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
12k 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 ...