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

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3answers
7k views

Find the equation of a circle given two points and a line that passes through its center

Find the equation of the circle that passes through the points $(0,2)$ and $(6,6)$. Its center is on the line $x-y =1$.
3
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1answer
338 views

Do the tangents of two circles define concentric circles?

Given two non-overlapping circles, $R_1$ and $R_2$. The radii of $R_1$ and $R_2$ may be different. The distance between the centers of $R_1$ and $R_2$ is defined as $x$. Draw the four tangents ...
0
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0answers
42 views

Zero cell formed by connecting n random points on a circle by chords

To start, think of a regular n-gon inscribed in a circle. If the vertices of the n-gon are all connected by drawing cords between the other vertices, then another smaller n-gon is created at the ...
1
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2answers
145 views

Simple question about circumference of circle

Q: The physical education teacher asked to one classroom, by vote, choose a sport between volleyball, basketball and football, to practice in class the following week. pie chart: The segment AB, ...
2
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1answer
303 views

Find the area of a circle that is NOT covered by the rectangle

Using the following image for a visual: Is there a formula or equation I can use to find the area of the circle NOT overlapped with the rectangle (i.e. the filled in orange part)? I know all of the ...
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2answers
122 views

Optimum fitting for flanges in a rectangular plate

I have a $2500~\text{mm}\times6300~\text{mm}\times25~\text{mm}$ (width $\times$ length $\times$ thickness) steel plate I want to cut flanges of diameter $235~\text{mm}$ can anyone please suggest $1)$ ...
6
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2answers
159 views

Circle Chord Sequence

This is my first post, so be nice! When I was in my first Geometry class in high school, I asked the teacher the following: Given a circle of radius 2a, find the length of the chord running parallel ...
1
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1answer
246 views

Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
2
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4answers
201 views

Proof of three points are enough to draw one and only one circle

Using the circle theorems or otherwise, I explained why the process locates the centre of the arc. However, I do not know what 'accuracy limitations of this technique' means. I don't think there is ...
5
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4answers
2k views

Newbie: determine if line *segment* intersects circle

I've read related posts, including: How to tell if a line segment intersects with a circle? where the suggestions are probably relevant, but above my level, and the final solution is actually not ...
1
vote
2answers
125 views

Determine counterclockwise moving

in my app, I let user touch and move to draw an arc. After drawing, I got a set of points. Is there any way to determine that user draw the arc counterclockwise or reverse counter clock wise?
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1answer
1k views

What is the area of the shaded part of the circle?

In the diagram below, line segment $AT$ is a diameter of the circle with center $O$. What is the area of the shaded part of the circle? $AT= 16$. Half of the circles area is equal to $100.48$, on ...
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0answers
157 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
0
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1answer
153 views

Drawing a triangle in a unit circle

This is a question that I derived for a long time ago. It asks if we draw a triangle in a unit circle does all arc lengths $(\alpha ,\beta ,\theta)$ and sides of triangle $(a,b,c)$ can be rational ...
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2answers
6k views

Determine center of circle if radius and 2 tangent line segments are given

Given the radius and its $2$ tangent lines and their point of intersection of a circle. A similar question is How to calculate the two tangent points to a circle with radius R from two lines given ...
9
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5answers
17k views

Area of intersection between two circles

Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres ...
2
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1answer
1k views

A unique circle with 3 points proof

I have prove the theorem: There is only one circle passing through three given non-collinear points in both geometrical and algebraic ways. THere is one question that I just have no idea with. 'the ...
12
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1answer
2k views

A hard geometry problem on circles

I found this problem on a website and I couldn't do anything. Do you have any ideas, hints? Edit: If I say $$\frac { { \partial }^{ 2 }f }{ \partial { a }^{ 2 } } +\frac { { \partial }^{ 2 }f }{ ...
3
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2answers
92 views

Two questions on clock arithmetic

I have two questions on clock arithmetic, both of which I have solved, but I am looking for neater proofs. Let us suppose we have a circle named $\mathbb{Z}_n$ with $n$ equally spaced points on it ...
1
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0answers
98 views

Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
6
votes
1answer
91 views

Area of circles: represent $x$ in terms of $r_1$ and $r_2$

See the image. Area of green and red regions are equal. Can you represent $x=|O_2D|$ in terms of $r_1$ and $r_2$ for $r_1> r_2$ ? Edit: The point $O_1$ does not enter in the region of small ...
1
vote
1answer
470 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
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2answers
59 views

Calculate Point based on distance in 2D-Space

I have a Point P in unit circle (on or in it) with a radius of r. How can I calculate a Point Q with a fixed radius of x, which has the same angle like P
2
votes
3answers
76 views

Drawing dynamic circles based on input value

Is there a formula that will allow me to calculate the radius of a circle based on an input value? The input value could be as small as zero or as large as $10^7$, or larger. The circle is ...
2
votes
1answer
481 views

Circle Packing: Unsolved Problem in Geometry?

Graham and Sloane minimize the second moment of the centres of a number discs in order to maximize their compactness. They use computational geometry techniques to find the optimal packings for ...
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3answers
274 views

Would a circle overlap a parabola's bottom by more than just its vertex?

I mean, out of the condition that a circle actually crosses the parabola. My question is when a circle is "inside" a parabola, would it touch part of the parabola other than just the parabola's vertex ...
2
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2answers
182 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
3
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2answers
7k views

What is a perimeter of a sector?

I don't under stand this. So we have: ...
0
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1answer
216 views

Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
1
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1answer
99 views

$\pi$ is just a number, or also the circumference of a sub-unit circle?

A unit circle defined in the Cartesian plane has a radius of $1$ and a diameter of $2$. So making a full round is $2 \pi$. Now, $\pi$ is the ratio of the circumference over the diameter, so if I have ...
1
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1answer
94 views

Circular motion trig

We have $x_P = -2 + 4 \cos (-\pi t)$ and $y_P = 1 + 4 \sin ( - \pi t)$ with $t$ in seconds. We have to find the coordinates of the intersection with the y-axis. So I use trig and I eventually end up ...
2
votes
0answers
140 views

Ellipse radius interpolation with different radiuses

I am writing a library for graphical LCDs and I want to incorporate a function to draw a circle on the screen. I have already succeeded in drawing simple circles, however, I want to be able to pass a ...
4
votes
4answers
6k views

Relation between chords length and radius of circle

Two chords of a circle, of lengths $2a$ and $2b$ are mutually perpendicular. If the distance of the point at which the chords intersect,from the centre of the circle is $c$($c<$radius of the ...
1
vote
1answer
139 views

Are the area of a circle inscribed in a square and the area of the “spandrels” (the four corners that remain) commensurable?

And how would you demonstrate that most simply? See the beginning of my blog post for a little more: http://seekecho.blogspot.fr/2013/02/different-ilks.html
2
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3answers
467 views

Geometry - Equilateral triangle covered with five circles

I have to cover an equilateral triangle (whose sides are 1m long) with 5 identical circles: what's the minimum radius of the circles?
3
votes
3answers
157 views

Marking the prime points on a circle

If you travel around a circle and mark all the points on the circle where the distance you travelled is a prime number, where you would go through many rotations*, do you end up marking the entire ...
1
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1answer
66 views

Homeomorphism on Identification Space

Let $\sim$ be and equivalence relation on the unit line $X=[0,1]$ defined by $x\sim y$ if either $x=y$ or $\textbf{both}$ $x$ and $y$ $\in$ {${0,\frac{1}{2},1}$}. Construct a homeomorphism ...
0
votes
1answer
136 views

How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
2
votes
1answer
64 views

Approximate radius of a group of n packed circles

I am looking for a formula to estimate the radius of a circle which would hold n number of circles with some radius r. I understand this is part of the packing problem which does not have a definite ...
2
votes
2answers
66 views

Could someone please explain the theory behind finding if a given point is inside a circle on a grid?

Let us say I have a grid of 1000 x 1000, and on that grid is drawn a circle, the circle could be anywhere. If I then pick a random point from the grid with an x and y co-ordinate I can work out if ...
2
votes
1answer
322 views

Center of circle that has two points on its circumference and a known tangent

I've found a related question, which helped me get started on this. I can get it to work for the example on the question, but I'm running into an issue when the tangent is not y = 0. Other question ...
1
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1answer
396 views

2D triangulation

I understood what it is from the following link: http://electronics.howstuffworks.com/gadgets/travel/gps1.htm But I want to know : In a 2D plane, if we know the (x, y) positions of three “guard” ...
1
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1answer
128 views

Two sticks between two concentric circles

Let's start with two concentric circles of radii $r<R$. Then we put two sticks inside the outer circle while avoiding the inner circle, say $AB$ and $CD$. Then we compare the length of inner ...
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3answers
3k views

Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
4
votes
2answers
341 views

Math Puzzle: Area of Concentric Rings

The problem below appeared on the latest round of Google Code Jam: Maria has been hired by the Ghastly Chemicals Junkies (GCJ) company to help them manufacture bullseyes. A bullseye consists of a ...
3
votes
2answers
191 views

Given a latitude how many miles is the corresponding longitude?

OK so lines of longitude (the distance/circumference around the earth horizontally) differ based on what latitude you are at (0 at north and south poles up to ~25k at the equator.) So given a ...
0
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1answer
245 views

Bounds of double integral given a circle and a line

Calculate the double integral of the area between the function $$x^2+y^2=25$$ and the line $$y=-x+5$$ in the first quadrant. Now, I am unsure how to choose the bounds for y, I understand that the ...
1
vote
1answer
101 views

Calculate points(x, y) within an arc

I am trying to draw lines from the center of a circle to points (x, y) in the circumference. To calculate this the angle is used. I need to render points in between two angles. E.g. Angle 0 to angle ...
1
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1answer
96 views

Calculating circle properties.

How can I incrementally calculate the angle from angle 0 and the point (x, y) in a circumference path if I have the center of the circle coordinates and the radius of the circle. I have 127 segments ...
1
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1answer
121 views

Similarity of triangles in a circle

The problem: c is a circle with a diameter AB. t is the tangent at the point B. Now C and D are two points on t and at different sides of B. I draw the line segments AC and AD, the point where AC ...