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

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10
votes
5answers
6k views

Calculate the area of the crescent

I found this problem on a thread on Stack overflow where it was posted as "job interview question". Unfortunately I cannot find the question. But I saved the picture and just cannot figure it out. ...
1
vote
3answers
8k views

Determine coordinate of intersection between a line and a circle

I'm putting together a simple script in processing to visualise layout possibilities within the fluid environment of a web page. I need some help calculating a point on a circle: The circle is as ...
4
votes
4answers
981 views

Area's of rectangle and circle

If a string with length of 20 cm was to create a rectangle and circle, would area of these objects be the same?
2
votes
2answers
682 views

subvolume area under the intersection of a plane (line) and a cone

I am implementing a conical filter for Gupta-Sproull anti-aliased line algorithm. Given a cone with the total volume of 1 and a radius of 1. Find the subvolume of the intersection of a line. The ...
96
votes
6answers
134k views

How many sides does a circle have?

My son is in 2nd grade. His math teacher gave the class a quiz, and one question was this: If a triangle has 3 sides, and a rectangle has 4 sides, how many sides does a circle have? My first ...
0
votes
1answer
114 views

Finding Two Touching circles with limited information

I am working on a track editor and have found myself in a situation where I need to define two touching circles. Ideally I would like to know the centre point, and radius of these circles. The ...
10
votes
1answer
312 views

Is there a way to represent the interior of a circle with a curve?

As you already know, the interior of a circle is represented by an inequality. For example, $$x^2+y^2\leq1$$ for the unit circle. Today I was thinking by myself and I wondered if there is a curve ...
2
votes
1answer
1k views

Positioning three circles, all of them touching each other

There are three circles, all of them touching each other. The bottom two circles are laying on an imaginary floor, such that they touch the line g=-r as well. Given are all three radii, r1 (A), r2 ...
5
votes
13answers
10k views

how to find center of an arc given start point, end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: start point (x0,y0), end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I ...
3
votes
1answer
3k views

rules for circle circumscribing

how can i determine wether a circle can be circumscribed about a quadrilateral?
8
votes
2answers
327 views

If $0$, $z_1$, $z_2$ and $z_3$ are concyclic, then $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear

If the complex numbers $0$, $z_1$, $z_2$ and $z_3$ are concyclic, prove that $\frac{1}{z_1}$,$\frac{1}{z_2}$,$\frac{1}{z_3}$ are collinear. I really can't seem to get anywhere on this problem, ...
7
votes
2answers
3k views

Inscribed kissing circles in an equilateral triangle

Triangle is equilateral (AB=BC=CA), I need to find AB and R. Any hints? I was trying to make another triangle by connecting centers of small circles but didn't found anything
0
votes
3answers
2k views

Formula to Move the object in Circular Path

I want to move one object (dot) in circular path. By using x and y position of that object. Thanks.
14
votes
1answer
2k views

How many circles to cover 2 times bigger circle?

How many circles (radius – r) are needed to cover circle which radius is 2 times bigger (radius – 2r). I think we need to use area which is $S=\pi R^2$ but I don't really know what to do
5
votes
2answers
711 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
309 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
2k 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
193 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
646 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
304 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
4k 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
339 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
1k 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
900 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 } ...
56
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
905 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 ...