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. D

    Tangential circles inscribed within a square

    In this diagram, a square is inscribed with four circles of equivalent size, all with the radius of 1. Each circle is tangent to two sides of the square, two circles, and the smaller circle. Obviously each side of the square is equal to 4, but what is the radius of the smaller circle? I...
  2. Loren Booda

    Avoid walking in circles in the wild

    Is there any general rule to avoid walking in circles in the wild?
  3. M

    Vertical Circles and Non-Uniform Circular Motion

    Homework Statement If we wanted to calculate the minimum or critical velocity needed for the block to just be able to pass through the top of the circle without the rope sagging then we would start by letting the tension in the rope approaches zero...
  4. P

    Trigonmetry Functions (radian circles)

    Homework Statement If sin (x) = -6/7 what is cos(x) = ? what is tan(x) = ? the answers have to be in integer form, as in no decimals. the "x" is supposed to be in quadrant 3 2. The attempt at a solution This is in radians so i did sin^-1 (-6/7) = -1.02969 the answer I am...
  5. S

    Ambiguous Problem involving Common Tangents to circles

    In my math exam , this question had appeared : http://img33.imageshack.us/img33/6233/44467585.jpg (You can click on the link to see the question) I'm having confusion as to what the answer to the question is. I feel that the correct answer to the question would be 2 Direct common...
  6. H

    Why Traffic Circles are Circular: Engineering Explained

    why is traffic circle only circular and not of any other shape.i mean i have heard answers like it makes traffic flow smooth and stuff but i want to know the actual reason something which involves engineering sense.
  7. W

    Find the Circles and Curves Problems

    1. A curve is traced by a point P(x,y) which moves such that its distance from the point A(-1,1) is three times its distance from the point B(2,-1). Determine the equation of the curve. A circle is tangent to the y - axis at y = 3 and has one x - intercept at x = 1. a. Determine the other x-...
  8. I

    Solving Problem with Circles in Backyard: Center (1,-1.5), Radius sqrt(29.25)

    In a backyard, there are two trees located at grid points A(-2, 3) and B(4, -6). The family cat is walking in the backyard. The line segments between the cat and the two trees are always perpendicular. Find the equation of the locus of the cat. My Answer: slope PA = (y - 3) / (x + 2) slope PB...
  9. L

    What Is the Radius of a Circle Tangent to the X-Axis?

    Here it is: A circle with center (–3,4) is tangent to the x-axis in the standard (x,y) coordinate plane. What is the radius of this circle? I have no idea where to start. I know there is some rule about tangency and circles, but I am unsure. Thanks!
  10. P

    Perimeter of a triangle which circumscribes by 3 circles

    Hello, I need help with this problem please (this is counted as large part of my grade so please hel) thank you Problem: Each of three congruent circles has radius 1, and each is externally tangent to the other two. An equilateral triangle circumsribes this configuration, so that each...
  11. A

    Common area between two circles.

    I am currently trying to figure out a problem in polar coordinates: Find the area common to the two circles x2 + y2 = 4, x2 + y2 = 6x. Using polar coordinates I know the two equations of the circles are r=2 and r=6 cos(theta) respectively. What I tried to do was find the area over the...
  12. W

    Homotopies between circles and paths in the annulus {z: 0<a<|z|<b }

    Hi, everyone : I read a problem posted somewhere else on showing that, "for the correct value m-- an integer" , any curve lying on an annulus A={0<a<|z|< b} was homotopic to the circle re^(i*pi*m*t). So I thought of this question: what are the homotopy classes of the annulus...
  13. Mentallic

    Calculating Pyramid Height from 3 Circles

    Given 3 circles each of radius r, stacked up into a triangular pyramid shape, find the height of the entire structure. This might be expressed more clearly in a graphical form: http://img206.imageshack.us/img206/3646/stackcircleseb0.png http://g.imageshack.us/img206/stackcircleseb0.png/1/...
  14. K

    2 5cm radius circles inscribed inside a 15cm circle

    Homework Statement 2 identical circles of radius 5cm touching each other externally and both are touching an arc length of a larger 15cm circle. Find the 1. perimeter and 2. area of the region between the 2 smaller circles and the arc length of the larger circle Homework Equations s=r...
  15. J

    Finding the center and radius of circles given an equation

    Homework Statement Find the center and the radius of the circle with the given equation. Homework Equations x2+y2+4y-117=0 The Attempt at a Solution I first got it in standard form by completing the square: x2+(y+2)2=121 but i don't know how to get the center and radius of...
  16. R

    Can the Midpoint Between Two Equal Circles Ensure Symmetric Area Division?

    Homework Statement There are two circles of equal radii. I have to prove that the mid point of the line joining their centres is the only point through which if several arbitrary lines are drawn, equal areas enclosed by the circles will fall on either side of the line. I cannot think of a...
  17. R

    Max Value of r1+r2 in Inscribed Circles of Semicircle

    Homework Statement There is a semicircle with radius 1. Two circles are inscribe in it with centres C1 and C2 and radius r1 and r2 respectively. Find the maximum possible value of r1+r2 Here is the picture, I have drawn. http://img143.imageshack.us/img143/8392/circlesdn3.png The Attempt...
  18. S

    Friction of a car going in circles

    Homework Statement A car that weighs 900 kilograms is driving around a racetrack, the radius of the racetrack is 100 meters. Thecar has a constant speed of 110 km/h. The friction coefficient between the tires and the track is 0.980. Decide: a) The car's acceleration b) The size of the...
  19. M

    Concentric Circles & Magnetic fields

    Homework Statement Figure a below shows two concentric circular regions in which uniform magnetic fields can change. Region 1, with radius r1 = 1 cm, has an outward magnetic field 1 that is increasing in magnitude. Region 2, with radius r2 = 2 cm, has an outward magnetic field 2 that may also...
  20. Ƒ

    Circles in Non-Euclidean Geometry

    Are circles considered straight lines in Non-Euclidean Geometry?
  21. M

    Points where tangent line touches 2 circles

    Homework Statement On the circles y^2+x^2=1 and y^2+(x-3)^2=4 There is a line with positive slope that is tangent to both circles. Determine the points at which this tangent touches each circle. Homework Equations the derivative of the first circle i found: y'=-x/y the derivative of...
  22. L

    Calculating Satellite Orbit Height Above Earth's Surface

    Homework Statement Communications satellites are placed in orbits such that they rotate the Earth once every 24.0 hours. Determine how high above the Earths surface these satellites must be placed. Homework Equations GM/4(3.14 squared) times T squared The Attempt at a Solution so i...
  23. A

    Area between two eccentric circles

    Hi, here is my geometry problem. I have two circles, one inside the other. The larger diameter is denoted by D, and the smaller by d. Their centers are eccentric by a distance e. Now, there is a line from the center of the smaller circle to the outside of the larger circle. I have derived an...
  24. Mentallic

    Plotting Cartesian Circles to Touch Unit Circle Once

    I have 3 circles, all cleverly plotted so as to touch the unit circle just once: x^2+y^2=1 (1) (x+1)^2+(y-1)^2=3-2\sqrt{2} (2) (x-\frac{\sqrt{7}}{2})^2+(y-\frac{1}{2})^2=3-2\sqrt{2} (3) What I need is a circle (in general form like those above) that touches all 3 circles just once...
  25. U

    Complex Circles: Path of |z-i| = pi

    Homework Statement I'm not sure how the graph looks like for the path |z-i| = pi Homework Equations I know that if the function is |z-i|=1 means a unit circle center at i The Attempt at a Solution Does that mean |z-i|=pi is a circle center at pi with a radius of pi? Thanks
  26. ZapperZ

    PF PHOTO CONTEST - Going 'Round In Circles (9/20-9/26)

    Going 'Round In Circles This week, your photos must be on things that goes 'round and 'round in circles. Zz. Contest Rules: 1. Any digital photo or digitally-scanned photo relevant to the theme will be accepted within the contest period. In case there's a gray area, or you're not...
  27. B

    limits, shirnking circles, points of intersection

    1. Homework Statement http://www.nellilevental.com/calc1.jpg 2. Homework Equations C1 = \left(x - 1\right) ^{2} + y^{2} = 1 C2 = x^{2} + y^{2} = r^{2} 3. The Attempt at a Solution Initially I thought that the "value" of R was just going to increase without bound since the...
  28. S

    How are the number of ball bearings in a roller bearing determined?

    Six circles fit tightly around one all of equal length, 12 spheres fit tightly around one sphere all of equal diameter. How many circles can fit around one which is 6 times the other circles diameter? How many spheres can fit around one sphere which is 6 times the diameter of the others?
  29. K

    Validity Using Euler Circles and Truth Tables

    I'm so confused on how to tackle this problem: 1. Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows: Let p be “The object belongs to set A. “Let q be...
  30. H

    Math problem about circles, graphs

    this is the question... For what values of k is the graph of the equation x^2 + y^2 +2x-4y+26=k^2 - 4k a. a circle b. a point c. an empty set i think i should change the equation to this form...(x+1)^2+(y-2)^2=k^2 - 4k - 29 then what?
  31. O

    Is it possible to rotate circles in 3D using coordinates and normals?

    I am creating a program where I want to rotate circles facing me(point sprites for those familiar with CG) so they look like spheres. Data I have: - coordinates of every point inside point sprite in [-1,1] € R^2 space. - center of point sprite in 3D space - point sprite normal in 3D space...
  32. F

    Circles & Parellel lines

    Homework Statement I'm having difficulty on this problem: "Two circles A, B ad a vector k are given. Determine points P on A and Q on B so that PQ is equal and parallel to k. ii) describe the situation where this is impossible" any body out there a master on circles, greatly...
  33. K

    Radius of Smallest Circle in 6 Circles Problem (10cm)

    If you inscribe 4 circles inside a bigger circle and then add another smaller circle, touching the other 4 circles, what is the radius of the smallest circle (in the centre) if the radius of the biggest circle is 10cm?
  34. I

    How do I construct a set of concentric circles with millimeter precision?

    How do I construct a set of "concentric" circles with millimeter precision? I would need a few real life circular objects with the following specifications: They should all be "semi-concentric" so that they all share the same central axis (at right angle to the planes of the circles), but...
  35. E

    Equations of circles tangent to graph

    Two circles of radius 3√2 are tangent to the the graph y^2 =4x at (1,2). Find the equation of each circle. I have found the derivative of the graph, which is 1/√x. I know that the equation of the circle is X^2 + Y^2=r^2 where r is the radius so the equation of each circle is X^2 + Y^2=18...
  36. O

    Identifying Equations: Parabolas, Circles, & More

    Homework Statement when asked to identify an equation as a parabola, hyperbolas, ellipses, circles, straight lines, or none of the above, how can i deduce which is which? the problems given are: 2x^2+2y^2=9 (im pretty sure this one's a circle, just by graphing it, but id like...
  37. R

    Double Integral of two concentric circles

    Homework Statement Let D be the region given as the set of (x,y) where 1 <! x^2+y^2 <! 2 and y !<0. Is D an elementary region? Evaluate \int\int_{D} f(x,y) dA where f(x,y) = 1+xy. Homework Equations The Attempt at a Solution So I understand that this is two concentric circles(an...
  38. P

    How Many Revolutions Does the Smaller Disk Make Around the Larger Circle?

    There are two disks of uniform density that touch at one point. their masses are in a ratio of 1:9. how many revolutions does the smaller disk make as it makes one rotation around the big circle? (assume that the disks do not slip) This is my try: a is small circle b is big circle...
  39. A

    Math help Circles and slope

    1.) How do you answer this? Find the equation of the line that has a slope undefined and passes through the points (3, -4). I got y=-4 ------------------------ 2.) Write the standard and general equations of the circle with radius 4 and center (1,2). I got STANDARD: (x-1)^2 +...
  40. J

    Circles of Light: Explore the Phenomenon

    Hello to whoever is kind enough to read this! A question, Suppose I place a rotating laser at the centre a circle so that the beam will hit the inner face of the circles circumference. If the radius of the circle is one light second, then the circumference would be 2pi light seconds...
  41. V

    Finding intersections of tangents on circles

    Homework Statement A circle, with a center at the origin, and a radius of 2 has at least one tangent with a slope of root3/3 and at least one tangent with a slope of -root3/3 . Calculate all intersection or intersections of these tangents Homework Equations The Attempt at a...
  42. I

    Limits, shrinking circles, points of intersection and love

    Homework Statement http://www.nellilevental.com/calc1.jpg Homework Equations C1 = \left(x - 1\right) ^{2} + y^{2} = 1 C2 = x^{2} + y^{2} = r^{2} The Attempt at a Solution Initially I thought that the "value" of R was just going to increase without bound since the slope of the line was...
  43. W

    Frenet-Serre Frames and circles.

    Hi, everyone: I am trying to show this: Given C(t) a unit-speed curve, using the usual Frenet-Serre frames T,N,B. Define the normal lines to C(t) to be the lines extending N, i.e, line segments containing N. Then: If all normal lines meet at a common point, C(t) must be part of a...
  44. Y

    Circles and prime numbers

    Some time ago I began playing around with packing circles and I have some questions that I am hoping someone here can help with. I have linked to three PDF files that should help in understanding my synopsis below. (You will need to click on the blank sheet and then open the PDF’s as I am...
  45. S

    Problem of overlapping circles

    A friend asked me the following question: Two circles with radii R and r are placed so that the one with radius r has its center on the circumference of the circle with radius R. How big should r be, so that the area of the overlap is exactly \pi R^2/2. The simple solution would be to insert...
  46. P

    Why Do Objects Move Outward When Spinning in Circles?

    This is what i don't get for things spinning in circles. So let's say you tie a mass to the end of a string, and you start swinging the string around in a circle with a constant speed. In the absence of air resistance, then the net force on the mass would be the centripetal force provided by...
  47. D

    Energy flux vector field problem is the isotherms are circles

    Homework Statement Suppose that the isotherms in a region are all concentric spheres centered at the origin. Prove that the energy flux vector field points either toward or away from the origin. Homework Equations J = - k (del)T The Attempt at a Solution so I know that -(del)T is...
  48. S

    Verical and Horizontal Circles

    This is a general question and one that I cannot get an answer for. What is the difference between the 2? How do they alter how we approach to solve a problem for each type? Answers kindly welcomed
  49. 6

    Around in unforeseen circles

    Is it possible that we have been (as the planet Earth) within the exact same space as we once had been? Meaning that, within all of our orbits around the sun, all of our trips around the galaxy, all of what we don't know about our relationships with other galaxies, and all of the countless...
  50. K

    Calculate Blue Surface Area of Circles and Rosette

    Homework Statement Find the blue colored surface area. 1 http://img338.imageshack.us/img338/1630/graph1zd7.png The radii of the circles are 3 cm and 1 cm. 2 Find the surface area of the rosette inside the equilateral triangle with side a. http://img87.imageshack.us/img87/2590/graph2dj9.png...
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