What is Circles: Definition and 308 Discussions

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The distance between any point of the circle and the centre is called the radius. This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted.
Specifically, a circle is a simple closed curve that divides the plane into two regions: an interior and an exterior. In everyday use, the term "circle" may be used interchangeably to refer to either the boundary of the figure, or to the whole figure including its interior; in strict technical usage, the circle is only the boundary and the whole figure is called a disc.
A circle may also be defined as a special kind of ellipse in which the two foci are coincident and the eccentricity is 0, or the two-dimensional shape enclosing the most area per unit perimeter squared, using calculus of variations.

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  1. I

    Need Help With Geometry Problem (Circles)

    In the diagram below: AB is the diameter of the semicircle with center O. Circles P and Q are tangent to each other and to the semicircle. If OB=4, find the radius of circle Q. I haven't been able to make any headway at all with this problem. I tried to find a system of equations with the...
  2. P

    Finding the (x,y) coordinates of arbitrary circles

    I have just started curiously thinking about this. The trig functions cos and sin give the (x,y) coordinates of the unit circle. How would i go about using the trig functions to finding (x,y) coordinates of an arbitrary circle? What I am saying is, the cos and sin only work for the circle x^2...
  3. S

    The crescent area created by overlapping circles

    Dear All, I need to know the area of the crescent created by overlapping circles;e.g. a circle radius 50µm overlapped by an equal circle with its centre 10µm to the left. Any help you can offer would be gratefully received, thanks.
  4. R

    Number of circles within a circle

    There are an infinite number of radii within any given circle, are there also an infinite number of circles within a circle as shown in the attached image ?
  5. H

    Show that the centers of the circles passing through the points

    Homework Statement Show that the centers of the circles passing through the points (3,2) and (6,3) are located on the line 3x+y=16. Two of these circles touch the line x+2y=2. Find the equation of both these circles. 2. Homework Equations The general equation of curves (circles...
  6. wolram

    Have the mysterious fairy circles of Namibia been solved?

    http://science.uniserve.edu.au/school/sheets/fairycircle.html I site i stumbled across, and just wondered if an explanation has been found.
  7. L

    Rotating integrals and circles

    kay had a question which i got zero on and now trying to figure out how the hell to do the question. Given x^2 + (y-1)^2 =1 rotated about the x-axis. if i could get the solution so i can review it so i can have a better idea how to do it on the mid term. Hint:, I was told to do with...
  8. C

    Solve Vertical Circles Problem: Find Roller Coaster Speed

    Here's the question. A roller coaster at an amusement park has a dip that bottoms out in a vertical circle of radius r. A passenger feels the seat of the car pushing upward on her with a force equal to twice her weight as she goes through the dip. If r=20.0 m, how fast is the roller coaster...
  9. S

    Area, Perimeter & Radius of Circles & Polygons

    This has been bugging me for a while and I thought that you guys might know an answer. Awhile ago I realized that there is a direct relationship between the radius (as in the distance between a corner and the center) squared and the area of any regular polygon with the same number of sides. For...
  10. S

    Length of the rope around two circles

    http://www.olemiss.edu/mathed/geometry/tight.gif To determine the shortest rope that can be wrapped around the two circles any ideas? i have forgotten everything about geometry. My nephew asked me this
  11. A

    Problem Solving question with circles

    1.what is the equation of the largest circle that can be incribed in a square of side length 9 units, if the diagonals of the square intersect at (-1,3). where the radious is 9, but the ansewer in wrong *** 2.Todd is flying his radio-controilled airplane abouve the ground in a circular path...
  12. L

    Can Trigonometry Be Applied to Circles with a Radius Other Than 1?

    I understand how trigonometry is related to the Unit Circle, but is there any way I can relate the same concept to circles with a radius other than 1? Thanks in advance. :biggrin:
  13. N

    Intersecting Secants Property and Two Circles of Unequal Radii

    i have a couple questions which i didnt want to continue on posting in the other thread or else it would get extremely hard to follow. 1. recall that the Intersecting Secants Property states that if two secants AB and CD intersect at an external point P, then PA x PB = PC x PD. well, i need...
  14. N

    Proving Equal Diagonals in a Quadrilateral Inscribed in a Circle

    1. A, B and C are points on the circumference of a circle, centre O, and ∠BAC=115°. Calculate the number of degrees in ∠OBC. I drew a diagram but could not come up with anything primarily because ∠BAC and centre O lie on opposite sides of chord BC (draw a quick diagram if you don't know what...
  15. S

    Speed of a bicycle - circles

    Suppose you ride a bicycle on a horizontal surface in a circle with a radius of 20 m. The resultant force exerted by the road on the bicycle (normal force plus frictional force) makes an angle of 15 degs with the vertical. a. What is your speed? b. If the frictional force is half its maximum...
  16. T

    Trig and Unit Circles: Solving cos pi(t) + sin pi(t) = 0 for pi(t)

    is it possible to solve cos pi(t) + sin pi(t) = 0 for determining the value of pi(t)?? pls help
  17. N

    Double Integrals and circles - Confirmation Wanted

    Hey, my Q is: "Integrate f(x, y) = Sqrt(x^2 + y^2) over the region in the x-y plane bounded by the circles r = 1 and r = 4 in the upper half-plane". Well, I firstly sketched out the region I get as my area in the x-y plane. I deduced that the ranges for x and y are: 0 <= x <= 4 Sqrt[1...
  18. B

    How Do You Calculate Chord Lengths in Intersecting Circles?

    Hello, i am having difficulty on a question involving chords i believe. what i have so far is: the length of CA is 17. therefore the length of CB is also 17 due to the fact that it is the radius of the first circle. the length of AD is 10. Therefore BD is also 10 because it is the radius...
  19. P

    Geometry (great circles)

    consider the 3 great circles C1,C2,C3 with respective normals (0,-1,1) (1,0,1) (1,1,0), and let f = Rc3Rc2Rc1 is f orientation preserving or orientation reversing. can i make a matrix using the normals... then calculate the determinate of A. and if its negative then its reversing and if...
  20. L

    What is the formula for finding the area of a sector in a circle?

    what is the formula to find a sector in a circle? so I'm given the radius and the arc of angle 60 degrees. To find the area in that arc, the forumla is something along the lines of: A=\frac{r^2}{2} * arc so... A=\frac{r^2}{2} * \frac{\pi}{3} is this right?
  21. P

    Confused on Orbits: Ellipses vs Circles

    As someone who only studied first year physics and maths and have taken no interest in it since than I was rather surprised to wake up one morning and realize along with 99.5% of the population that I really had no idea how the planets orbits worked beyond the vague word ellipse which I didn't...
  22. E

    Intersecting circles in 2D: find some coordinates

    I have two circles intersecting at 2 points in 2d space. Let's call them cirles O1 and O2. On O1, I have 3 points A,B and D. On O2, I have a point C. Given co-ords of only 3 points A, B, C, and value of angle ADC (alpha), how can I find out the coord values x,y of point D ? Thanks :blushing:
  23. T

    Does Distance from Center Affect Acceleration in a Spinning Disk?

    If I take a perfectly rigid disk 10 miles in diameter and set it spinning at a constant speed. Is the constant acceleration an object experiences riding 5 feet from the center the same as it would be if it were 5 miles from the center? I know many other things would be different but I mean the...
  24. C

    How Can You Calculate the Arrangements of Red and White Roses in a Circle?

    How many orders can we have of 3 red roses and 3 white roses arranged in a circle? Apparently the answer is 10 - but how do yiou work it out? I know that in a circle of "n" different objects the number of different arrangements is (n-1)!, but what about the repeats? If anyone could explain a...
  25. D

    Help needed with calculating distances from circles

    I'm looking to find someone who can help me with my problem... My problem is that I need to remove material from linear tapered strips with a 1 inch round cutter. The circles need to connect to each other at half the section depth over the entire length of the strip --->...
  26. wolram

    Exploring Crop Circles: Is There More Than Meets the Eye?

    I know that crop circles have been discussed to death but, has all the data gleaned from the investigations of these anomalies shown that they are hoaxes ie the node explosions?
  27. L

    To show that equivalence classes of ker f are concentric circles

    I just want to make sure that I am doing this right or if I am on the right track. To find a map f :R ---> R so that ker f ={(x,y): x^4=y^4} pi_R: (x,y) ---> {(x,y): x^4=y^4} pi_R: x ---> {R(x): x^4 is an element in X} pi_R: Y ---> {R(y): y^4 is an element in Y} Define f: R x R --->...
  28. T

    Learn About Circles & Find Radius

    circles... and pie ok so i found this site and I am learning about circles now :) http://www.mathgoodies.com/lessons/vol2/circumference.html it says pie is 3.14 which is what you get when you divide the outer measurement of the circle by the diameter (pie being 3.14 as per his homework)...
  29. recon

    Theorems Related to Max Sums & Perimeters/Areas of Circles

    I need to know the names of theorems related to the following two problems: 1. What is the maximum sum less than 1 but more than 0 that can be formed from \frac{1}{p} + \frac{1}{q} + \frac{1}{r}, where p, q and r are positive integers? 2. What is the maximum perimeter and area of an...
  30. A

    Special triangles and Unit Circles HELP

    If sin theta = \frac {-4} {7} and \frac {3 pi} {2} < theta < 2 pi then determine the exact value of \frac {1} {cot (theta)} I don't know where to start I know to set up a circle with a cartesian plane but what am I supposed to do? :uhh:
  31. R

    Fun Problem: Area of Overlapping circles

    Picture two indentical circles with their radii overlapping. They form an intersection, what is the area of their intersection? I solved it the calculus route and it can be solved geometrically. Have fun.
  32. S

    How many circles can fit inside a circle?

    A circle with the radius R cuts the centers of circles with the radius r that does mearly touch each other, What is the equation for the number of circles in the circle?
  33. J

    Circumscribed and inscribed circles of a regular hexagon?

    Hey ppl, Could anyone help me with this: what is the ratio of the areas of the circumscribed and inscribed circles of a regular hexagon? how do I go about working it out from first principles? Cheers, joe
  34. E

    Someone good at math triangles and circles?

    Sorry to bother you guys.. but if there is someone out there that is good at math and wouldn't mind helping me.. could you aim me sn:"euphoriet" thanks.
  35. J

    Calculating area of intersecting circles

    Hi All, I went to this website where someone wants to know how to calculate the area of some intersecting circles in this diagram on the page. I took Geometry and Trig but unfortunately my brain turned to mush over the summer and I can't remember how to do this, can someone here tell me how I...
  36. G

    Coordinate geometry - circles.

    I'm just introducing myself to coordinate geometry in the xy plane of cirlces. Here's a question I'm having trouble with: Q11: The line with equation y=mx is a tangent to the circle with equation x^2 + y^2 - 6x - 6y + 17 = 0. Find the possible values of m. At first i thought i'd try...
  37. S

    Find Largest Dropping Circle in Parabola & x^4 Graphs

    Here's an interesting problem (interesting to me, at least) that my professor gave me last year (outside of class...it had nearly nothing to do with the subject we were studying). It's of two parts: The first part is fairly simple. Suppose you have the graph f(x)=x^2. What is the radius of...
  38. I

    Crop Circles: Fact or Fiction?

    Does anyone here take some crop cirlces seriously? http://paranormal.about.com/library/weekly/aa021802a.htm
  39. T

    Crop Circles: Astonishing Phenomenon or Mass Media Trickery?

    What you guys think of crop circles? The latest one are astonishing and I don't imagine people on the ground hoaxing them. Maybe we are being manipulated by mass media and those crop circles are produced using computers by Hollywood specialists? Earliest crop circles I admit were made by...
  40. Ivan Seeking

    'Fairy circles' of Africa baffle scientists

    \http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2004/05/10/wcirc10.xml&sSheet=/news/2004/05/10/ixworld.html
  41. M

    Help with Questions: Circles, Vectors, Wedges & dv/dt=g-kv

    Hey, I’d appreciate some help with these questions: (c) Find the centre and radius of the circle x^2 + y^2 – x – y – 12 = 0. Find the equations of the tangent to this circle which are parallel to the line 7x – y = 0. Ok, so I found the line has a slope of 7, and the circle has a...
  42. H

    Solving Trig Problem: 4 Tangent Circles, Find Shaded Radius

    Trig Question Any ideas on solving this problem? The question reads... Four mutually tangent circles are shown. Find the radius of the shaded circle. See attachment. Any help will be appreciated. :confused:
  43. J

    God can't make square circles.

    I am not very well versed in math, but I do have some idea, would this theorem be correct? Basis Step: x is an element of the universal set. In other words, you could say that the number 5 is an element of N(the set of natural numbers), and it is also in the set of R (the set of Real...
  44. J

    The Golden Spiral - Calculating intersections with circles.

    The "Golden Spiral" - Calculating intersections with circles. Hello all, I am working on a program that graphs the Golden Spiral and then lays a set of circles on top of it. I was curious to know if there is a formula I can use to figure out the x, y coordinates where a circle of a given radius...
  45. S

    Circles in a Box: Forces on Uniform Spheres at 35* Angle in Fixed Container

    Two identical uniform spheres, each weighing 75 N are at rest on the bottom of a fixed rectangular container. The line of centers of the spheres makes an angle of 35* with the horizontal. Find the forces exerted on the spheres by the container bottom, the container sides as well as the force...
  46. D

    Electricity Circles question that's killing me

    Heya Folks, First I would like to apologize for my bad English - I live in Israel and our mother toungue is Hebrew here, I'll try my best though.. Now I don't know how you call what we call Straght-Line Electricity Circles but basically I mean AC just not alternative ;) Anyways my...
  47. Loren Booda

    Density of circles centered on like circumference

    Imagine a circle of given radius. Construct all circles of equivalent radii whose centers constitute that initial circumference. Can you derive a probability density that describes the overall distribution of points from those resultant circles?
  48. ShawnD

    How can I integrate and find the moment of inertia for a circle?

    In school, I'm doing this thing called moment of inertia given by the formula I = \int y^2 dA If the object being solved for is a rectangle where the base of it is parallel to the x axis, dA is equal to xdy. From there, the integration is easy. If the object to solve the integration for is...
  49. S

    A pair of two-dimensional supercompressed circles

    Imagine a two dimensional universe, a plane. We take two perfect circles on this plane; they are uncompressable, being elementary particles or some such thing (whatever they are, the important thing is that they cannot be compressed). We take these two circles and set them on a collision...
  50. C

    The truth about crop circles

    Does anyone know it, or have good guesses? I'm not particularly interested in the subject per se, but I find it strange that the skeptical explanation (that it is a hoax) is as phoney as the claims that ET's do it. As far as I can tell no one seems to know what is going on, and yet everyone...
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