# Questions tagged [circles]

For questions concerning circles. A circle is the locus of points in a plane that are at a fixed distance from a fixed point.

698 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
472 views

### How to calculate the average distance between two points in concentric annuli

I tried to solve this analytically but gave up and ran a simulation. I would still like to know if it can be done explicitly. Consider a circle radially divided into 'zones', so say zone 1 is the ...
43 views

### Degree measure of circles

One slice of a circle which has been divided into 360 slices is one degree right? If this is the case, won't bigger circles have bigger slices and therefore bigger degrees? Why is one degree of a ...
63 views

### Equation for the points touching a circle.

In the plane $\mathbb R^2$, a point $P$, a point $M$ and the radius $r$ are given. Suppose, that $|\overrightarrow {PM}|>r$. Then, there exist two tangents from $P$ to the circle with mid point $M$...
404 views

### Calculate new pitch and roll after rotating about the z axis

I am wanting to know how to find out the new pitch and roll values when rotating around a circle. I have become a little stuck on how to achieve this, but hopefully someone will be able to point me in ...
78 views

### Triangle side-length problem

my problem is the following. A triangle ABC is given. P is a point on $\overline{AB}$. $k_1, k_2, k$ are the radii of the in-circles of APC, BPC, ABC. $s_1, s_2, s$ are radii of the ex-circles of ...
394 views

### Find the Langitude and Longitude of the centre point of a circle given a point on the circumference.

I couldn't find a similar question! Given I have the latitude and longitude (x,y) of a point on the circumference of a circle, and I want the circumference to be 1000m. An example of a lat lang I ...
77 views

### Graphing Circles, Ellipses, Parabolas, and Hyperbolas

I need help plotting a curve on a graph where the distance from focus1 is always the same ratio to the distance from focus2. For instance, lets assume focus1 is -5 along the x axis, and focus2 is +5 ...
242 views

This question somehow is unsolvable to me. Any idead/hints wil be much appreciated. $AB$ is a chord which is cut ny the chords $CD$ and $EC$ in the circle. Givens: $\frown{AC} +\frown{BE}=\frown{AD}... 1answer 253 views ### What is the curve's name for the “reciprocal” equation of a circle? The equation of a unit circle is $$(x-a)^2+(y-b)^2=r^2$$ When the origin $$(a, b)=(0,0)$$ the equation becomes $$y=(1-x^2)^{1/2}$$ Naturally when this equation is plotted on graph paper we get a ... 0answers 252 views ### Packing circles in circle vs semicircle vs quarter of circle Consider$N$disjoint circles with radius$1$packed into a larger circle$C$. Let$R$be the smallest possible radius of$C$, allowing the best packing density. Now take the$N$unitary circles ... 1answer 857 views ### From any arbitrary point$P$on$y =\cos x$tangents$PA$and$PB$are drawn to a circle which passes through From any arbitrary point$P$on$y =\cos x$tangents$PA$and$PB$are drawn to a circle which passes through the points$(1,0)$and$(3,0)$and touches the circle$x^2+y^2-2x-8=0$and have its ... 0answers 171 views ### The Biggest Smallest Piece to Smallest Biggest Piece ratio of a circle cut by n chords with maximal number of regions It is well known that a circle cut by n chords gives at most (n^2 + n + 2 )/2 regions eg. http://mathworld.wolfram.com/CircleDivisionbyLines.html Questions:- How close to equal area regions can we ... 0answers 88 views ### To find a fifth degree equation by using circles and lines that cannot be solved by radicals An example quintic whose roots cannot be expressed by radicals is$x^5 - x + 1 = 0$. I asked a geometry question about a fifth degree equation long time ago . I had an equation in the question. It ... 1answer 349 views ### Mapping a distorted ellipse onto a circle I have a circular label pasted on a cylindrical object. In the image, this circle looks like a asymmetrical ellipse. I know the radius of the cylinder and that of the label. What mapping do I need to ... 0answers 3k views ### Rounding Corners: How to calculate Fillet radius? How do I find the maximum rounding I can apply to either corner for any amount of rounding on the other corner? The all circles are perfect circles, but I can't figure out the max size of the ... 2answers 727 views ### Square covered with circles I have a square 800x800 and i need to fully cover it with the least number of circles possible, each circle has a radius of 150. QUESTIONS: - What pattern would be the best to use? Clover, diamon or ... 0answers 96 views ### Probability of a certain circular configuration Pick each of$n$angles ,$\theta_1$through$\theta_n$, uniformly randomly in the range$[0,2\pi$]. Define the distance$d_{i,j}$between$\theta_i$and$\theta_j$by$d_{i,j} = \min(|\theta_j - \...
379 views

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 ...
235 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 ...
822 views

### Drawing a Great Circle between two given points on Earth

I need to draw a great circle arc between two latitude and longitude points. For sake of example we will use the coordinates for LAX and JFK. JFK is 40.64°N / 73.78°W LAX is 33.94°N / 118.41°W My ...
160 views

### How to constrain disks that intersection of them is inside unit circle

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ ...
150 views

### Circles tangent to a parabola

For the past two weeks I was struggling with solving the following problem. Description of variables: $(x_n,y_n)$ - center point of the circle $C_n$ $r_n$ - radius of the circle $C_n$ Given the ...
543 views

### Interval and Circle

Can anyone give me a proof of why the circle $S^1$ and the closed interval $[0,1]$ are not homotopically equivalent? (Using the basic definition and not the fundamental group!)
37 views

### What are the conditions required for the perpendicular bisectors of all sides of a quadrilateral to intersect?

What are the conditions required for the perpendicular bisectors of all sides of a quadrilateral to intersect? Actually, this question came in my mind while I was thinking about how a circle can ...
71 views

### Expected overlap of n circles of equal area randomly placed inside a circle of larger area

Say I have an outer circle of area $\Omega$. If I randomly position n circles of area $\omega$ ($0 \le \omega \le \Omega$) completely inside the outer circle, then what is the expected overlap area of ...
16 views

### Semi-Conjugacy and the preservation of wandering intervals

This is mostly a checking of my understanding. Currently I am working through the proof of Denjoy's Theorem in Katok and Hasselblatt's Introduction to the Modern Theory of Dynamical Systems, and ...
31 views

42 views

### Probability of obtuse triangles formed on a circle

There are 16 equally spaced points on the circumference of a circle. If 3 points out of these 16 points are selected randomly, What is the probability that they will form an obtuse angled triangle?
23 views

### What is the coordinate value after moving counterclockwise by distance $d$ from a coordinate on the ellipse?

Let me define an ellipse function as follows: Assuming $a \ge b$, $$f(x,y) = \frac{(x-x_0)^2}{a^2} + \frac{(y-y_0)^2}{b^2} = 1,$$ where $(x_0,y_0)$ is the origin of the ellipse, and $a$ and $b$ are ...
44 views

### Calculating point on circle given angle and distance traveled without calculating radius

I want to calculate the X,Y coordinates of a point on a circle given only the distance and angle traveled, without calculating the radius as an intermediate step. My starting point (0,0) is at the ...
62 views

### Approximation for the equation of an imperfect circle

Given two random points $(x_0,y_0)$ and $(x_1,0)$ and some condition, I have an equation $C[(x-x_0)^2+(y-y_0)^2]=[(x-x_1)^2+y^2]^2$ which is a perfect circle if I ignore the power (2) on the RHS. ...
72 views

### Problem about incentre of a triangle.

Through the incentre $I$ of triangle $ABC$ a straight line is drawn intersecting $AB$ and $BC$ at points $M$ and $N$, respectively, in such a way that the triangle $BMN$ is acute- angled. On the ...
47 views

Is there a symbol to denote, say, $ABCD$ is a cyclic quadrilateral? (I very much doubt it.)