Tagged Questions

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

learn more… | top users | synonyms

5
votes
2answers
221 views

Center and radius of circle question

For a circle that has the equation $(x-a)^2 + (y-b)^2 = r^2$ , I know it has center $(a,b)$ and radius $r$. But what happens if the equation is $x^2 + (y-b)^2 = r^2$ ? With $b$ not equal to $0$ and ...
2
votes
1answer
389 views

Concentric circles(IMO 1988/Problem 1)

Let us consider 2 concentric circle radii R and r (R > r) with centre O.We fix P on the small circle and consider the variable chord PA of the small circle. Points B and C lie on the large circle; ...
0
votes
2answers
302 views

Finding centre and radius of circle

Let $a,c \in \mathbb R$ with $a \neq 0$, and let $b \in \mathbb C$. Define $$S=\{z\in \mathbb C: az\bar{z}+b\bar{z}+\bar{b}z+c=0\}.$$ a. Show that $S$ is a circle, if $|b|^2 > ac$. ...
11
votes
5answers
15k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
1
vote
2answers
373 views

How can I find an upper bound for the radius of an arc, given arc length and chord length?

This is similar to this question, except I am finding the radius now using the Bisection method and then Newton's method for finding a zero. This is a computer science for a Numerical Methods course. ...
2
votes
2answers
448 views

Calculating point on circle after time

I have a question that seems very similar to calculating-point-around-circumference-of-circle-given-distance-travelled and calculating-point-on-a-circle-given-an-offset, but I don't believe they are ...
1
vote
1answer
380 views

A plane Geometry Problem

The triangle $ABC$ has $CA=CB$, circumcenter $O$ and incenter $I$. The point $D$ on $BC$ is such that $DO$ is perpendicular $BI$. Show that $DI$ is parallel to $AC$.
4
votes
2answers
367 views

Problem on circles- Plane Geometry

The chord CD of a circle center O is perpendicular to the diameter AB. The chord AE goes through the midpoint of the radius OC. Prove that the chord DE goes through the midpoint BC.
0
votes
1answer
105 views

circle that touch quadrantal internally

I want to know how to construct circle that touch quadrantal(1/4 part of circle) internally. I spend several hours for solving this problem but I have no luck. I attached the picture what I've ...
4
votes
1answer
180 views

Determine if circle is covered by some set of other circles

Suppose you have an existing set of circles $\mathcal{C} = {C_1, .., C_n}$ each with a fixed radius $r$ but varying centre coordinates. Next, you are given a new circle $C_{n+1}$ with the same radius ...
0
votes
1answer
114 views

How do you express how much a curve or part of a circle is “bent”?

Given a certain curve, or part of a circle, how do you express how much it is bent? If I have for example 1/3 of a circle (without seeing the full circle). How do I calculate and express that it is ...
8
votes
2answers
468 views

Coloring a sphere with minimum colors (with constraints)

This is a problem we've been considering in our undergraduate math club, and I thought it would be nice to get further thoughts on the subject. I will start with a two dimensional case and then ...
1
vote
2answers
108 views

Is circle formula same in different XY system?

I want to check an element if it's in a circle in my browser. I know the circle formula from my high school: But I'm not sure if it's same in browser XY system too. Because browsers zero ...
1
vote
1answer
1k views

Area of a square using circle

So I have this square and theres a circle inside of it. The circle of radius $r$ is inscribed in the square. So how do I find the area of the square in terms of $r$? I know that area of a circle is ...
0
votes
1answer
163 views

What is the ratio of the area?

If the segment A'B' is tangent to the incircle of triangle ABC, and that segment AB = segment CM; then, what is the ratio of the area of the triangle ABC to the area of the small triangle A'B’C? ...
0
votes
0answers
255 views

A section of the circle's ring

What is the simplest way to calculate the area of the blue section of the circle's ring shown below using the following datas : a) K is the center of the square ABCD, b) Vertices A and C are on the ...
0
votes
2answers
171 views

Algorithm to randomly place circles at least $D$ distance away from one another

I'm trying to work out how to write an algorithm to randomly place circles of $R$ radius, in a 2d rectangle of arbitrary dimensions, such that each placed circle is at least $D$ distance away from ...
1
vote
0answers
93 views

How to determine the center of a circle with pen and straightedge [duplicate]

Possible Duplicate: Determine the centre of a circle My buddy draws a circle then he erase its center. He quiz me how can find the center with only pen and straightedge (no compass). Do ...
2
votes
3answers
640 views

what formula describes the convex hull of two circles (i.e. two circles connected by tangent lines)?

I'm investigating the following problem. Imagine a circle at the origin with radius r. The circle moves upward with speed s and its radius simultaneously increases by a length of b per time unit. ...
5
votes
1answer
294 views

Is this concept of circle geometry known?

Astonishingly, no mathematician ever could give a "Mr. Foobar invented this" whenever I came up with this construction, although it is very elementary. Given are 3 circles C1,C2,C3 (avoid degenerate ...
4
votes
2answers
385 views

rotating 90 degrees around a circle on a co-ordinate plane

I thought the answer would be square root of 3. It would seem that the x co-ordinate of Q would just be the opposite of the x co-ordinate of P. I'm not sure if the picture is just being ...
2
votes
2answers
443 views

Chord dividing circle , function

Two chords PA and PB divide circle into three parts. The angle PAB is a root of f(x)=0. Find f(x) Clearly , PA and PB divides circle into three parts means it divides it into 3 parts of equal areas ...
1
vote
2answers
3k views

Calculating point around circumference of circle given distance travelled

Its the end of the day and my brain just cant cope anymore. Can anyone help with, what I hope, is a simple question.. Given a point on a circle (x, y coordinates) how can I calculate the coordinates ...
2
votes
1answer
94 views

Finding the location of the end of an arc, knowing the beginning, the arc's length and the radius

I apologise in advance if this is really basic. I have a circle of radius 15, from which i work out an arc, given an angle of arbitrary value (it's for a computer program). Given that i know the point ...
3
votes
2answers
289 views

Circle bitangent angles

Say we have two circles $C_1$ and $C_2$ with radii $r_1$ and $r_2$, respectively. Let their centers be $d$ units apart. There are 4 bitangents, two outer and two inner. Examine the intersection of an ...
2
votes
4answers
3k views

line segment joining two centers of circles is perpendicular to line segment joining two intersection point of the circles

Prove that the line segment joining the two centers of the concurrent circles of equal radius is perpendicular to line segment joining the two intersection points of the circles. I had come across ...
3
votes
2answers
1k views

Area Between Three Circles of Differing Radii

From the link in wikipedia http://web.gnowledge.org/wiki/index.php/Area_Between_Three_Circles_of_Differing_Radii OPEN QUESTION: What is the equation, in three variables, relating the radii of ...
6
votes
3answers
2k views

Definite integral: $\displaystyle\int^{4}_0 (16-x^2)^{\frac{3}{2}} dx$

The following integral can be computed using the substitution $x = 4\sin\theta~$ and then proceeding with $dx = 4\cos\theta~ d\theta~$, and evaluating the integral of $\cos^4\theta~$: ...
0
votes
3answers
512 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
5
votes
1answer
255 views

What is the mathematical principle that describes a series of dots on concentric circles that form a spiral pattern?

Apologies for the vagueness of the question, I'll clean it up once an answer helps me describe it better. I'm fascinated by the pattern demonstrated in this image. It's made up of dots on a series ...
6
votes
4answers
3k views

Can a circle truly exist?

Is a circle more impossible than any other geometrical shape? Is a circle is just an infinitely-sided equilateral parallelogram? Wikipedia says... A circle is a simple shape of Euclidean geometry ...
6
votes
3answers
93 views

Algorithm to determine if a collection of unit discs covers the unit disc centered at the origin?

I have a list of points $ (x_i, y_i) $ for $i = 1...n$. Is there an algorithm to determine if the union of the unit discs centered at these points is a superset of the unit disc centered at $(0, 0)$? ...
0
votes
4answers
5k views

How do you find the formula for an area of the circle through integration?

I got this question on my Maths exam today, and the Department of Education has stated it is on the syllabus, but none of the three textbooks I could get my hands mention anything about it. One ...
1
vote
3answers
720 views

Inscribed kissing circles in an isosceles trapezoid

5 equal circles in an isosceles trapezoid. Radius of circle is 4. Find black colored area. I don't have any ideas, could you give me a hand? Thanks.
13
votes
1answer
226 views

A question on circles

Given that a lamp-post can light a surrounding circle of radius 100 m, what is the minimum number of such lamp-posts required to light a circular ground of radius 1000 m.
4
votes
2answers
366 views

Geometry Question: Calculating the length of the side of a triangle inside a circle

Given this picture: The radius of the circle is $30$ inches. The angle between $A$ and $B$ is $22.5$ degrees. How would I calculate the distance (not along the arc, but straight line) from $B$ to ...
2
votes
1answer
713 views

How to check if circles intersect each other?

I'm trying to do trilateration where I know the coordinates of three known points and the estimates of the radii - not guaranteed to be really precise. My question is, how can I check if the circles ...
4
votes
1answer
254 views

How do I find the intersections of 2 circles on earths surface?

I have the circles' center in lat & long, as well as the radius in meters. How do I find the circles intersections? Edit: EXAMPLE: ...
2
votes
1answer
364 views

Generating a random point on the unit circle

I'm trying to figure out a way to generate a random point on the unit circle in an application I am developing (I'm a programmer). So far I have the following (in pseudo-code), where Z is a random ...
2
votes
2answers
2k views

Counting number of distinct regions with intersecting circles

Given $n$ circles of possibly different radii, how many distinct regions can there be? For small $n$, I can work it out with pictures. (I'm pretty sure $n=4$ can yield 13 distinct regions, but not ...
8
votes
2answers
8k views

Finding the intersecting points on two circles

Given 2 circles on a plane, how do you calculate the intersecting points? In this example I can do the calculation using the equilateral triangles that are described by the intersection and centres ...
6
votes
2answers
1k views

How do I calculate the equation of a circle given 3 complex numbers?

Given three complex values (for example, $2i, 4, i+3$), how would you calculate the equation of the circle that contains those three points? I know it has something to do with the cross ratio of the ...
5
votes
3answers
431 views

Find sagitta of a cubic Bézier-described arc

I have a situation where I have an arc that was mangled (irrelevant: by c#'s GraphicsPath.AddArc() function). The original arc is guaranteed to be circular, and the new data I have describes the ...
0
votes
1answer
714 views

Get the relation between X and Y axes in triangle based on the degree between

I have a given degree (0 - 360), and based on it, I'd like to be able to calculate the length of X and Y axis of a triangle built on that angle , if the third side of that triangle is equal to 1. I ...
9
votes
1answer
3k views

How many dimensions does a circle have?

Is a circle just a line (therefore 1 dimension) or is it a 2-dimensional object because it occupies some surface? Thanks in advance!
2
votes
2answers
2k views

Area of a circle externally tangent to three mutually tangent circles

Given 3 equal circles, with 3 points of intersection. The line between two of these intersecting points is 3 feet. They are inside a 4th circle. All circles are tangent to each other. What is the ...
13
votes
2answers
579 views

Covering the plane with disks

How to prove that it is impossible to cover the plane with disks? /The disks are closed disks and two disks can meet (at most) at only one point (obviously on the border)./ Thank you very much in ...
10
votes
5answers
5k views

Calculate the area of the crescent

I found this problem on a thread on Stack overflow where it was posted as "job interview question". Unfortunately I cannot find the question. But I saved the picture and just cannot figure it out. ...
1
vote
3answers
7k views

Determine coordinate of intersection between a line and a circle

I'm putting together a simple script in processing to visualise layout possibilities within the fluid environment of a web page. I need some help calculating a point on a circle: The circle is as ...
4
votes
4answers
962 views

Area's of rectangle and circle

If a string with length of 20 cm was to create a rectangle and circle, would area of these objects be the same?