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

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2
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2answers
530 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
votes
1answer
404 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
votes
3answers
954 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 ...
1
vote
3answers
750 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
votes
1answer
1k 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
votes
1answer
279 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 ...
5
votes
3answers
2k 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?
1
vote
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 ...
0
votes
1answer
282 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.
1
vote
2answers
569 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 ...
3
votes
2answers
15k 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 ...
3
votes
1answer
4k 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 ...
-1
votes
1answer
190 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 ...
1
vote
1answer
968 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 ...
1
vote
1answer
437 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 ...
4
votes
1answer
197 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 ...
1
vote
2answers
239 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 ...
1
vote
4answers
493 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 ...
1
vote
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 ...
5
votes
1answer
3k 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 ...
1
vote
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 ...
6
votes
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 ...
1
vote
0answers
107 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 ...
1
vote
1answer
74 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 ...
1
vote
2answers
452 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.
2
votes
2answers
1k 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 ...
0
votes
1answer
931 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 ...
0
votes
1answer
158 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 $y_\text{max}$.
0
votes
1answer
136 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 ...
1
vote
1answer
587 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
votes
0answers
613 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
votes
1answer
747 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
votes
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 ...
7
votes
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.
0
votes
1answer
424 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 ...
1
vote
2answers
231 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 ? ...
1
vote
0answers
260 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
votes
4answers
4k 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
votes
1answer
570 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 ...
0
votes
2answers
434 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 ...
1
vote
2answers
149 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 ...
1
vote
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? ...
4
votes
0answers
479 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 ...
7
votes
4answers
323 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?
2
votes
1answer
172 views

Similar Right Triangles and Incircles [duplicate]

Possible Duplicate: Triangle and Incircle In a setup of right triangles ABC, BDA, and BDC not unlike this diagram (click on the link, and ignore the written side measures and subtext in ...
1
vote
4answers
711 views

Finding the equation of a circle

$A=(3,1)$ and $B=(-1,-1)$ are points on a circle of center $(k, -3k)$ find the value of $k$ I begin by assinging the values $\ g = -k $ and $\ f=3k $. I then substitute $(3, 1)$ and $ g= -k, f= ...
0
votes
1answer
98 views

Finding a point which is constrained to 3 other points.

Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points? Similar to this question, but with non-fixed minimum ...
0
votes
3answers
5k views

Circle and Line segment intersection

I have a line segment (begin $(x_1,y_1)$, end $(x_2,y_2)$, with $D=5$, let’s say) and a circle (radius $R$, center $(x_3,y_3)$) How can I check that if my line segment intersects my circle? picture ...
1
vote
2answers
229 views

Closest point to a unit circle from a point inside it

I'm working on a code at the moment that calculates the closest point to a circle from a point inside it. Let's say we have the point ($x_0, x_1$) to calculate the closest point to the unit circle it ...
0
votes
1answer
407 views

Determine larger arc from smaller arc

Given two angles (the starts and end of an arc), e.g. 90 degrees to 180 degrees, I need to output the starting and ending degrees of a small arc, and a large arc. In this case the small arc is simply ...