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

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3answers
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Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
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2answers
59 views

rates of motion of projected points along a circle

Have I forgotten all my secondary-school geometry? (That's not actually my question.) Suppose $R>r>0$ and consider this circle (later edit: I think $R>0$, $r>0$ is enough; we don't ...
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1answer
557 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
2
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1answer
628 views

Finding points relating to the edge of a circle in an x,y coordinate system

My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
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1answer
234 views

Find a circle that is tangent to a line and a circle.

I need to find the circle that will be tangent to a line at a given point and a circle. The diagram below hopefully makes it clearer. The known data are: points P2,P3,P4,P5 Circle C2's radius r ...
2
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2answers
382 views

Connecting two tangents with two circles of equal radius

In a cartesian system I have 2 lines (an input and an output) and want to find the radius (r) and centre (c1, c2) of the two circles of equal radius that are touched tangentially at the end point of ...
5
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1answer
219 views

Rotation $x \to x+a \pmod 1$ of the circle is Ergodic if and only if $a$ is irrational

I have a book, Ergodic problems of classical mechanics by Arnold/Avez, and in it they prove that rotation $Tx = x+a \pmod 1$ of the circle $M=\{x \pmod 1\}$ is Ergodic if and only if a is irrational. ...
2
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3answers
706 views

3-D equation of a circle

I came across a sum but could not solve it as i dont know the 3d equations of a circle : The sum is If $A(3,-2,2)$ and $B(2,9,5)$ are the end points of a diameter of a circle,then the third pt that ...
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3answers
621 views

angle of an inscribed triangle

I have a scalene triangle inscribed in a circle, one of its sides $a$ is $2\sqrt3$ and the length $r$ from that side to the center is $1$. I need to find the angle $x$ opposite to the side given. ...
7
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1answer
736 views

How to turn this sum into an integral?

I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
2
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1answer
263 views

Convergence and closed form of this infinite series?

If we have a circle of radius $r$ with an $n$-gon inscribed within this circle (i.e. with the same circumradius), we can find the difference of the areas using: $$A_n =\overbrace{\pi r^2}^\text{Area ...
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3answers
1k views

Average distance between two points in a circular disk

How can I find an average distance between two points lying inside a circular disk of a certain radius? I wonder if there is any other way except of using a Monte Carlo method?
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5answers
3k views

Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator?

Evaluate the $\sin$, $\cos$ and $\tan$ without using calculator? $150$ degree the right answer are $\frac{1}{2}$, $-\frac{\sqrt{3}}{2}$and $-\frac{1}{\sqrt{3}} $ $-315$ degree the ...
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1answer
258 views

Finding the measure of $\angle AEB$ given a figure

In the given figure, $O$ is the center of the circle and $$ \angle AOB =120$$ How could I find the measure of $\angle AEB$? Thanks in advance.
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2answers
500 views

Find the radius of the circle?

Three circles of equal radii have been drawn inside an equilateral triangle , of side a , such that each circle touches the other two circles as well as two sides of triangle. Then find the radius ...
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2answers
11k views

Distance Between Any Two Points on a Unit Circle

As part of a larger investigation, I am required to be able to calculate the distance between any two points on a unit circle. I have tried to use cosine law but I can't determine any specific manner ...
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1answer
3k views

How does this equation to find the radius from 3 points actually work?

I had searched online and found an equation that solves the radius of a circle from 3 points that are located on the circumference of that specific circle. Where I had found this formula did not state ...
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1answer
185 views

How to find the area. Linked with another question. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? In this question we discussed why the fake proof is wrong. But, what about the area? The process converges to the same area of the circle ...
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1answer
691 views

internally and externally tangent circles

See the diagram here: diagram The diagram shows two circles of radius 1 and 2 tangent to each other and internally tangent to a circle of radius 3. What is the radius of the outlined circle ...
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0answers
152 views

Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum

I want the calculate the "value" of an angle in such a way that: The angle of 45 degrees corresponds with the maximum value of 1 The angles of 0 and 90 degrees correspond with the minimum value of 0 ...
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1answer
357 views

Meaning of this 4x4 determinant

Let $p,q,r$ and $s$ be four points on the plane. Moreover, $p,q,r$ are given in clockwise order. My book said that the following determinant is positive if and only if $s$ lies inside the circle ...
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1answer
180 views

Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
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2answers
194 views

Find the ratio in which the circle divides each of the sides AB and AC?

A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint . Find the ratio in which the circle divides each of the sides AB and AC? Does the line ...
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4answers
328 views

What is the radius of the circle in cm?

The rectangle at the corner measures 10 cm * 20 cm. The right bottom corner of the rectangle is also a point on the circumference of the circle. What is the ...
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3answers
1k views

Find the radius of the circle?

Two Circle of an equal of an radii are drawn , without any overlap , in a semicircle of radius 2 cm. If these are the largest possible circles that the semicircle can accomodate , then what is the ...
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1answer
2k views

Closest point on circle edge from point outside/inside the circle

Alright, I am programming a plugin for a game that requires me to get the closest point on a circle when all you have is a point B, which is outside of the circle, the radius of the circle, and the ...
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3answers
3k views

Find the length of the common chord

"Two circles with centres C1 and C2 and radius 6 cm and 8 cm respetively cut each other at right angles. Find the length of the ...
5
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1answer
3k views

Integer solutions (lattice points) to arbitrary circles

Wolfram Alpha will provide integer solutions to arbitrary circle equations. I'm trying to understand how it's able to calculate them, but despite a fair bit of digging I haven't found any discussion ...
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0answers
102 views

contradicting PI=4 fallacy. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? I know that you can take area out of a square without changing it's perimeter. Now, here's this problem: Draw a circle with dia = 1; Draw a ...
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1answer
69 views

Computing angle

See the drawing for the situation. Given lenghts a, b and c and also L, but k and angle alpha are unknown. How to compute this angle alpha? I know it is possible to compute if we first compute k in ...
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2answers
424 views

Given an angle, get the trigonometric circle point.

Given an angle, in degrees, how can I get the trigonometric circle point coordinates for it? For instance, given the angle 0, I would get (1,0). 90 would be (0,-1). Clockwise.
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votes
2answers
932 views

Calculate radius of variable circles surrounding big circle.

I got a circle, which I know all the details about him. (Radius [100], Diameter [200], Circumference [628.32], Area [31415.93]...) I would like to surround this circle, with smaller circles. I know ...
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1answer
857 views

Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
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1answer
123 views

Function for the upper left part of a circle

What is the function corresponding to the upper left quarter of a circle ? Where $x$ goes from 0 to $x_\text{max}$, and $y=f(x)$ goes from $y_\text{min}$ to $y_\text{max}$.
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1answer
118 views

Circle : How to get all co-ordinate list of circle parimeter?

I want to find all the co-ordinate of circle. I know the radius of circle and considering center co-ordinate as (0,0). So Is there any equation for finding all ...
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1answer
520 views

Tough Geometry Problem--Regular Polygon inside Circle

$ABCDEFG$ is a regular heptagon inscribed in a unit circle centered at $O$. $\ell$ is the line tangent to the circumcircle of $ABCDEFG$ at $A$, and $P$ is a point on $\ell$ such that triangle $AOP$ is ...
3
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0answers
533 views

Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
3
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1answer
668 views

How do you find the angle of circle segment formed with points (x,y) and (radius,0)?

I've been learning about the unit circle, sine, cosine, and the like in my introduction to trigonometry course, but I'm drawing a blank here. If I have a circle centered at the origin, with radius r ...
3
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1answer
2k views

Packing squares into a circle

I need determine the maximum number of squares of the given size that can be packed into a circle of the given radius. Squares can be rotated. I'm not sure how complex this problem is and i can find ...
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4answers
2k views

I need a proof that a line cannot intersect a circle at three distinct points

I need a simple proof that a line cannot intersect a circle at three distinct points.
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1answer
368 views

equation to get 10 points on circle surface at fix distance

What I tried is : $$x = \sin(36 \cdot 50 \cdot 3.14)/180$$ $$y = \cos(36 \cdot 50 \cdot 3.14)/180$$ Here $36$ is because I want 10 points on circle so $360/10=36$. $50$ is center X and center Y ...
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2answers
219 views

Area of a circle

I've tried to find as a personnal exercise where the formula $A=\pi R^2$ comes from. After drawing the problem, I've found that $A = 2\int\limits_{-R}^{R}\sqrt{R^2-t^2}dt$. How can I calculate this ? ...
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0answers
246 views

What “boundary conditions” can make a rectangle “look” like a circle?

I posted the question below in Stackoverflow but then realized that it perhaps would find a better audience here. I am solving a fourth order non-linear partial ...
3
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4answers
3k views

How to calculate the two tangent points to a circle with radius R from two lines given by three points

I need to calculate the two tangent points of a circle with the radius $r$ and two lines given by three points $Q(x_0,y_0)$, $P(x_1,y_1)$ and $R(x_2,y_2)$. Sketch would explain the problem more. I ...
3
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1answer
501 views

finding one circles radius so that it tangentially touches two other set circles

I am designing a water fountain on google sketchup and have run into a problem. I am designing the contours of the stone in the fountain. I would attach a picture of the problem but i need 10 ...
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2answers
428 views

Position of 3 circles intersecting at the centre of bounding box

Here's what I feel is a neat challenge: I'm building a data visualization comprised of 3 circles of dynamic sizes. I want to have them all intersect at the centre of a bounding box that will also be ...
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2answers
144 views

Trigonometry & circle math

I tried to solve this Trigonometry question, but I do not know how to solve. I read that the circle has radius 1 and center at (0.0) as the unit circle is plotted in the coordinate system. I ...
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1answer
2k views

how can I obtain enclosed area between two circles in cartesian coordinates?

In the diagram below (from here fig.2, page.5) the enclosed area between two circles (shaded area) has been indicated $a_{t+\delta_{t}}$. Can anyone help me how can I compute this? is it true? ...
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0answers
348 views

Pinwheel- perimeter of semicircular region

Above, we have a larger circle of $r=16$ with 8 equally spaced semicircles of radius=8. Each semicircle has one end on the larger circle's center and the other on the circumference of the larger ...
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4answers
305 views

Does the graph of $\cos x$ intersect the unit circle other than the point (0,1)?

It would seem the unit circle is nicely tucked under the graph of $\cos x$, touching only at (0,1), but is that what's truly going on here?