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

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0
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2answers
57 views

Compute the integral over the volume of a torus,

In $\mathbb R^3$, let $C$ be the circle in the $xy$-plane with radius $2$ and the origin as the center, i.e., $$C= \Big\{ \big(x,y,z\big) \in \mathbb R^3 \mid x^2+y^2=4, \ z=0\Big\}.$$ Let $\Omega$ ...
-2
votes
3answers
25 views

Finding the equation of a circle given 3 points without using elimination [on hold]

find the equation of the circle using points (-4,-4) (-3,1) (2,0) without using elimination.
1
vote
2answers
26 views

Two circles touching a line and the axes

If the circle $C_1$ touches x-axis and the line $y=x \tan\theta$,$\theta \in (0,\frac{\pi}{2})$ in the first quadrant and circle $C_2$ touches the line $y=x \tan\theta$,y-axis and circle $C_1$ in such ...
0
votes
0answers
20 views

Non intersecting chords. [duplicate]

This was a question in a math contest and it just blew me. We are given n points on circle, without any coordinates and radius. Our aim is to derive an expression in n for number of ways in which: ...
3
votes
2answers
20 views

Does the radius of the quadrant pass from the center of the inscribed circle?

In the following picture: The smaller circle is inscribed inside the quadrant, whose radius (OB) is 8. The original question (but not the question of this post) is that "find the radius of the ...
2
votes
1answer
45 views

One special case of Helly's theorem (for $\text{radius}=1$ circles)

There are $n$ points on the plane. Any $3$ of them can be covered with a radius $1$ circle. Prove that there is a radius $1$ circle that covers all the points. Came to this when tried to prove an easy ...
0
votes
0answers
12 views

Find Intersection of Two Circle given Lat/Lon and radius

I am attempting to calculate the intersection of two circle on the Earth with a given latitude, longitude and radius. I started with this post. While I am using this in the context of programming, it ...
2
votes
1answer
38 views

Circle bisecting the circumference of another circle

If the circle $x^2+y^2+4x+22y+l=0$ bisects the circumference of the circle $x^2+y^2-2x+8y-m=0$,then $l+m$ is equal to (A)$\ 60$ (B)$\ 50$ (C)$\ 46$ (D)$\ 40$ I don't know the condition when one ...
0
votes
1answer
29 views

3 Points in 3D Space to Develop an Arc or Circle

Background: I'm a Robotics Engineer and I am trying to develop a more flexible, modular, and robust program for our welding robots, which will minimize teaching time for new robots and also minimize ...
1
vote
3answers
54 views

How can I find the co-ordinate of where a line intersects a circle?

I was looking to know if there was an equation that would allow me to calculate the co-ordinates of a point on the circumference of a circle where a line intersects it and the center. My diagram ...
2
votes
5answers
73 views

Find the equation of the circle.

Find the equation of the circle whose radius is $5$ which touches the circle $x^2 + y^2 - 2x -4y - 20 = 0$ externally at the point $(5,5)$
1
vote
1answer
72 views

Are ther situations when 3 points do not lie on a circles?

Consider 3 points on a plane, points are real. Is it possible that the points are placed in a way that makes it impossible to draw a circle trough them. I know that if the point forms a line then ...
0
votes
1answer
11 views

Find point on circle's tangent based on point on circle, radius and angle

The circle is centered at (0,0)"P" with a radius of 5. I have a point on the circle at (4,-3)"A". How would I find the points "B1" and "B2" on the tangent through point "A" given an arbitrary angle ...
0
votes
0answers
24 views

Determine clockwise or anticlockwise

I have a central point define by an x and y and I have an object which is moving around it with a location defined by an x and a y. I'm trying to determine if the object is moving clockwise or ...
0
votes
2answers
52 views

given 3 circles, find relation of the regions

I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard. I had no idea how to find it nor where to start Note ...
1
vote
2answers
60 views

What is the homeomorphism between a disk and an ellipse?

A disk/circle is defined by $$C = \{(x,y) \in \mathbb{R^2} : x^2 + y^2 \leq r^2\}$$ An ellipse is defined by $$E = \{(x,y) \in \mathbb{R^2}: x^2/a^2 + y^2/b^2 \leq 1 \}$$ How can we define a ...
0
votes
1answer
62 views

Calculating another point on a circle from radiants

I have a program that tells me the angle in radians of a cursor from another item, let's say it's a star. What I want is to take this $(X_2,Y_2)$ point and deviate it a bit on the left or right ...
0
votes
3answers
28 views

Scalene triangle with semicircles mensuration

I was recently going through a mensuration sum from a tenth grade board exam book. This one particular question stumped me, and I spent the entire evening thinking of this, but to no avail. The ...
0
votes
1answer
14 views

Creating Polynomial Function with Surface Area of Cylinder

I've spent a few hours at this question but can't seem to get the right answer. I was hoping someone here can lead me in the right direction. The question: A storage tank is to be constructed ...
2
votes
3answers
60 views

Drawing circumference issue

I'm a developer, and I'm developing an app on Google Maps. At the moment, I'm trying to draw a circle on the map. For getting all the points I need, I'm using the following formula: \begin{equation} ...
2
votes
4answers
120 views

how to prove that the circle $(x-a)^2+(y-b)^2=a^2+b^2$ is passing through point $(0,0)$

How can one prove that the circle $(x-a)^2+(y-b)^2=a^2+b^2$ is passing through point $(0,0)$? I know that if i put: $x=y=0$, i will get: $(0-a)^2+(0-b)=a^2+b^2=a^2+b^2$ But that's not a proof but ...
1
vote
1answer
33 views

Angle of intersection of the given curves.

What is the angle of intersection of $$[|\sin x| + |\cos x|]$$ And the curve $$ x^2 + y^2 = 5 $$ where $[n]$ denotes greatest integer function. This is a homework question. I have tried to find the ...
0
votes
1answer
67 views

Two circles defining a line

We have two dots $d_1,d_2$ moving on circles $C_1, C_2$ with radii $r_1, r_2$. The circles are moving at speed of $s_1, s_2$. A line is drawn between $d_1$ and $d_2$. When does this line have some ...
1
vote
0answers
36 views

An equivalent definition of the rotation number of a circle homeomorphism

Let $f : \mathbb S^1 \to \mathbb S^1$ be an orientation-preserving homeomorphism. The classical definition of the rotation number is the following: we lift $f$ to a homeomorphism $F : \mathbb R \to ...
0
votes
2answers
32 views

Find a bisector point of a circle

The coordinates of $A=(x_{0},y_{0}$) and $B=(x_{1},y_{1}$) are given. How to find the coordinates of $C$ and $D$ as per given information below. ABC is equilateral triangle such that $AB=BC=CA$ ...
0
votes
1answer
39 views

What is the area of the shape defined by the locus of a point on a circle rolling around another circle?

What is the area of a shape, which I'm deeming a 'cylicoid', which is defined as follows: Circle A of radius 1 is held stationary. Circle B of radius 1 has a point on its rim which traces a path as it ...
1
vote
1answer
35 views

Equation for spacing of elements on the edge of a circle

I'm trying to come up with an equation which, given an index within an arbitary number of elements (the most natural example would be 12, as in 12 numbers on a clock), along with an arbitrary radius, ...
0
votes
2answers
44 views

Help me find the point of intersection of a line and a point. [duplicate]

Find the equation of the circle with its center at $(-1,-3)$ and tangent to the line through the point $(-2,4)$ and $(2,1)$. The line is $3x+4y=10$ and the point is $(-1,-3)$. What's the better ...
0
votes
0answers
25 views

Area of equilateral triangle from circumcircle

I am trying to calculate skewness of triangle. Given the sides of a triangle (not equilateral), I calculated circumradius from which I would like to get area of equilateral triangle.
-1
votes
5answers
54 views

distance between centres of two overlapping congruent circles

If there are two overlapping congruent circles such that the area of intersection is 10% of the area of each circle, what is the distance between their centres in terms of the radius r cm?
2
votes
4answers
102 views

What is the direction along the edge of a circle called (in English and by chance German)?

Note: I am actually also searching for the term in German. That is why I posted this here (as opposed to the language SE's), besides me looking for this term in a mathematical/technical context. ...
1
vote
1answer
38 views

Surface area of the circle

I was told to calculate the surface area of the following circle by the integration method (monte carlo) $x^2 + y^2 = 1$ The area of this circle is determined by the following inequalities: $-1 ≤ x ...
5
votes
0answers
36 views

Proof of the Inscribed Angle Theorem

I want to give a proof of the Inscribed Angle Theorem by using the Laguerre formula. Let $C$ denote the circle. Take three different points $A,B$ and $P$ on $C$. Write $a := \overline{AP}$ and $b:= ...
0
votes
1answer
26 views

Can a rotating circle fill all sides of a rotated rectangle?

Consider we have a fixed rotating circle and a rotating rectangle which is forced to be tangent with the circle. Does circle travel all points of rectangle's Perimeter?
0
votes
1answer
29 views

how to find the space of one circle minus the second circle

I got two circles c1 and c2 with the same radius and different center. The two circles overlapped. How to calculate the space in C1 without the overlapped section with C2.
0
votes
0answers
106 views

Descartes Circle

Having two fixed circles and one varying circle, how can I find the radius of nth circle if the new circle formed acts as varying circle i.e. a and b are radius of two fixed circle. using them and ...
0
votes
3answers
34 views

Algorithm for intersection of n circles with approximate values

I'm trying to come up with a sort of trilateration algorithm that, given n >= 3 circles, finds the point of intersection. The radii come from samplings of electromagnetic magnitudes, therefore there ...
4
votes
1answer
47 views

Plot of $n$ concentric circles at once?

While we plot the Equation of $$(x^2+y^2-1)=0$$ we get: While we plot $$(x^2+y^2-4)=0$$ we get: So What will happen if we plot $$\prod\limits_{i=1}^{i=n} \Big({(x-a)^2+(y-b)^2-i^2}\Big)=0$$ ...
5
votes
4answers
147 views

Circle revolutions rolling around another circle

I just watched this video, and I'm a bit perplexed. Problem: ...
2
votes
1answer
75 views

inscribed circle in $n$-gon

If I'm given a circle with radius $r$ and I want to create a polygon with side $n$ (say $n=5$) which can cover the circle fully, then how to prove that a regular polygon is the solution with minimum ...
1
vote
1answer
331 views

Apollonian gasket

Okay , is there a way to find the radius of the nth circle in a apollonian gasket .. Something like this Its like simple case of apollonian gasket .. I found from descartes' theorem $R_n = ...
0
votes
0answers
30 views

How to scale x- and y- axes equally in Maple?

I have the ellipse $\frac{25}{36}x^2+\frac{5}{36}y^2=1$. Maple draws it as a circle: How can I change the coordinates, to make it look like an actual ellipse?
-1
votes
2answers
33 views

Euler's formula for off-center circle [closed]

A circle with radius $R$ and center at $(a,b)$ is given by the formula $(x-a)^2 +(y-b)^2 = R^2$. A circle with radius $R$ whose center is at the origin is given by Euler's formula: $R e^{i \theta}$. ...
14
votes
6answers
2k views

How is the area of a circle calculated using basic mathematics?

Area of a circle is addition of circumference of layers of a onion. If n is radius of a onion then area is $$ A = 2 \pi \cdot 1 + 2 \pi \cdot 2 + 2\pi \cdot 3 + \ldots + 2 \pi \cdot n $$ which $$ ...
1
vote
1answer
25 views

List all sets of points in a plane that are enclosed by circles with given radius

My problem is: Given N points in a plane and a number R, list/enumerate all subsets of points, where points in each subset are enclosed by a circle with radius of R. Two subsets $S_i$ and $S_j$ should ...
-2
votes
3answers
117 views

Circles in circle

If we are given one big circle and infinite amount of smaller circles with equal radius (of course radius of the smaller is < radius of the big one) and we have to put in the center of the big ...
13
votes
1answer
294 views

How big is my pizza, if I know its slices' sizes?

I bought a box of frozen pizza: eight slices, baked and then frozen, stacked in a box. The packaging assured me that I was holding an 18-inch[-diameter] pizza. That got me thinking: how do I know ...
3
votes
1answer
42 views

Conversion between trig functions and hyperbolic trig functions

Using trig identities we can see that $\sin^2 x + \cos^2 x = \tanh^2 x + \text{sech}^2 x = 1$ , and so the parametric graph $(\cos t, \sin t)$ is similar to $(\text{sech} t, \tanh t)$. The first ...
0
votes
1answer
33 views

Area of intersection of two Annulus

Given two separate annulus with centers $[C_1,C_2]$ and their corresponding radii being $[R_1,r_1]$ and $[R_2,r_2]$ respectively, larger radius being $R$. There are methods to look at whether they are ...
1
vote
1answer
33 views

Find corners of a square in a plane in 3d space

I am given two angles (similar to theta and phi in spherical coordinates) from which I can calculate a normal vector to a plane in 3d space. I am also given the center point of the square and the area ...