What is Circle: Definition and 1000 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. Akash47

    A geometry problem with a circle and a bisected radius

    I have tried a lot by angle chasing e.g. let ∠ABC=x° then ∠ACB=90°-x°. As AU=AV=radius of circle so ∠AUV=∠AVU=45°. I've connected U,D and V,D. Then ∠UDV=135° etc. But I haven't found any way to get near of proving AE=DE. I have also tried to prove 'the area of triangle AEU= area of triangle...
  2. kaloyan

    Find this angle given the triangle's Orthocenter

    ##AD## is diameter, thus ##\angle ACD = \angle ABD = 90^\circ##. Also ##HBDC## is a parallelogram because ##HC||BD, HB||CD##. It seems useless and I don't know how to continue. Thank you in advance!
  3. W

    MHB Circles in a square and diameter of the circle

    A circle is inscribed in a square with sides = 40. A smaller (of course!) circle tangent to the above circle and 2 sides of the square is inscribed in one of the corners of the square. What is the diameter of this circle?
  4. J

    Shortest path to a point that doesn't pass through the given circle

    This is my attempt at a solution. Point A is the center of the circle (6,8) and Point B is the given point (12,16). I believe that the shortest path would be the one that is equal to the sum of CE and EB or its symmetrical complement. (I forgot to put a point where the top line intersects the...
  5. S

    Fortran Generate a circle in FORTRAN having polar coordinates

    Say "I have grid in polar coordinates (r, theta). How do I plot it in tecplot. Tecplot plots it in cartesian coordinates."
  6. K

    B "Onion proof" of the area of a circle

    https://en.wikipedia.org/wiki/Area_of_a_circle#Onion_proof I understand the basic concept, although it is a little difficult to visualize the thin discs close to the centre of the circle. Regarding the area of each disc, it is given in the link above as 2πrdr. Then, by means of integration...
  7. JD_PM

    Why the magnetic field doesn't have to describe a circle?

    Homework Statement Imagine an infinite straight wire pointing at you (thus, the magnetic field curls counterclockwise from your perspective). Such a magnetic field equals to: $$B = \frac{\mu I}{2 \pi s} \hat{\phi}$$ I want to calculate the line integral of ##B## around the circular path of...
  8. G

    MHB Tangent line to circle making 30º with a second circle

    Hi all, this is my first thread! I am having problems trying to find the way of drawing a line which is tangent to a circle and intersects another circle making a 30º intersection. Let´s say I have circle A with coordinates 479183.87, 4365099.87 (x1,y1) and a radius of 27780m. I have a second...
  9. Yasin

    Maximum Angular Velocity of a quarter circle

    Homework Statement Finding the general formula for max angular velocity ( answers say 0.839*(g/b)) but I do not understand how Homework Equations 0.839*(g/b) The Attempt at a Solution
  10. E

    Circumference of Circle with Uncertainty

    Homework Statement Calculate the circumference (including uncertainty) of a circle whose measured radius is r=7.3 ± 0.2cm. 2.Relevant equations & 3.The attempt at a solution - Circumference of circle --> C = 2πr = 2π7.3 = 45.87 cm - Exact constant error propagation --> z =...
  11. D

    I Parity operator and a free particle on a circle

    Hi. I have just looked at a question concerning a free particle on a circle with ψ(0) = ψ(L). The question asks to find a self-adjoint operator that commutes with H but not p. Because H commutes with p , i assumed there was no such operator. The answer given , was the parity operator. It acts...
  12. S

    Swinging Ball at Top of Circle: Forces & Energies

    A 0.160 kg ball attached to a light cord is swung in a vertical circle of radius 70.0 cm. At the top of the swing, the speed of the ball is 3.26 m/s. The centre of the circle is 1.50 m above the floor. a. Draw a free-body diagram of the forces on the ball at the top of the swing. b. Calculate...
  13. M

    I Parameterize a circle based on the contact angle with a wedge

    Hi PF! Given a 2D plane, the following is a parameterization of a circular arc with contact angle ##\alpha## to the x-axis: $$\left\langle \frac{\sin s}{\sin\alpha},\frac{\cos s - \cos\alpha}{\sin\alpha} \right\rangle : s \in [-\alpha,\alpha]$$ However, I am trying to parameterize a circle...
  14. A

    I Paradox: Rocket ship moving in a circle

    Say there is a circular fence that has a diameter of 10 meters, and a rocket ship that is normally 20 meters goes very quickly so that its relativistic length is 1m from the position of an observer standing at rest with relation to the fence. The rocket ship starts to go in a circle inside the...
  15. V

    I How to think of S1 (circle) abstractly

    Im having a bit of trouble when it comes to what the abstract object S1 actually is. Often in a book they will mention a parametrization of the circle in the complex or real plane. But this requires embedding the circle in Euclidian space. How should one think of the object S1 without thinking...
  16. E

    MHB Find the areas of segment in circle

    So far i have. 14) area of sector is πr²/3 = 12π length of chord. that triangle has two sides of 6 and angle of 120º split the triangle in two right triangles with angle of 120/2 = 60 and hyp=6. other (longer) side is: sin 60 = x/6 s = 6 sin 60 = 6(√3/2) = 3√3 third side is s = 3 cos 60 =...
  17. E

    MHB Find the area of sector in a circle in terms of pi. (Geometry)

    So far i have 270/360× (pi)r^ i don't know what to do next please help.
  18. E

    MHB Find radius, circumference, area and arc length in circle

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  19. Krushnaraj Pandya

    Equation of a circle from given conditions

    Homework Statement Equation of the circle passing through the point (1,2) and (3,4) and touching the line 3x+y-3=0 is? Homework Equations x^2+y^2+2gx+2fy+c=0...(1) (-g,-f)=center of circle sqrt(g^2+f^2-c)=radius...(2) The Attempt at a Solution Putting (1,2) and (3,4) in equation 1 we get...
  20. Math Amateur

    MHB Graphs of Functions Covering Unit Circle .... Hubbard & Hubbard, Example 3.1.5 .... ....

    I am reading the book: "Vector Calculus, Linear Algebra and Differential Forms" (Fourth Edition) by John H Hubbard and Barbara Burke Hubbard. I am currently focused on Section 3.1: Manifolds ... I need some help in order to understand Example 3.1.3 ... ... Example 3.1.3 reads as follows:In...
  21. M

    Vertical Circle (Circular Motion)

    Homework Statement You swing a 1.60m long string with a metal ball attached to its end in a vertical circle, such that the speed of the ball does not change but the rope is always taut. The tension in the string when the ball is at the bottom of the circle is 60.0N more than the tension when...
  22. M

    MHB Optimizing Fuel Usage on a Circular Route with Squares: A Mathematical Proof

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  23. N

    MHB Unit Circle Problems solve cosW=sin20, sinW=cos(-10), sinW< 0.5 and 1<tanW

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  24. S

    Circular Motion: Swinging a rock on a string in a vertical circle....

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  25. R

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  26. Navin

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  27. KristinaMr

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  28. M

    Y=cx[L−x], The value of the constant c for a perfect circle

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  29. N

    Find the center of a circle given a tangent line & point

    Homework Statement "Find the center and radius of the circle that passes through A(1,1) and is tangent to the line y=2x-3 at the point B(3,3). (Picture of the graph: https://imgur.com/a/0wAnqcU) Homework Equations Here's a link: https://imgur.com/a/y71Z9GY The Attempt at a Solution Soo, I've...
  30. R

    MHB Proving Shortest Distance Between 3 Points on a Circle

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  31. Mathman2013

    Maximum area of a fenced-in half a circle

    . Homework Statement Let imagine you have gras field formed as a semi circle and you want to fence in that area. The fence is connected to a wall, so you only have to fence in the area formed by the semi-circle. You have to use 60 meters of fence bought at a hardware store. Homework...
  32. Osvaldo

    I Circle tangential velocity approaching c

    When a merry go rounds tangential velocity approach c, and horses look closer than when at rest, what is reduced, angular velocity or radius?
  33. M

    A thin steel plate is in the shape of a half circle

    Homework Statement The half thin steel plate has a radius of 4 meters and a surface density of (3+r) kg/m^2, where r is the radial distance from the origin. Using calculus, find: A. its area B. its mass C. Its center of mass with respect to the origin shown, D. It's rotational inertia about the...
  34. Pushoam

    Determining maximum and minimum points of a projected circle

    Homework Statement Homework EquationsThe Attempt at a Solution This problem belongs to the topic "calculus of variation ". The fundamental problem of “calculus of variation” is to find a function y(x) such that the integral ## I = \int_{x_i }^{ x_f} \phi (y’, y, x) ~d x ## is extremum...
  35. P

    Limits to accelerate a spacecraft by spinning it in a circle

    The basic concept is to have your space probe(s) - likely nanocraft [1] on a spinning object in space which allows you to preserve the momentum you give it while accelerating it faster. Then once you are at a speed you can simply release the nanocraft in the direction you want it to go in. More...
  36. M. M. Fahad Joy

    Find the Area of the Shaded Section in a Circle

    Known data: In the picture, CD = 10 cm. What is the area of shaded area? Equation: I know, Area of a circle = ##πr^2## Diameter of a circle = ##2πr## Attempt: Here, ## r = 10/2 = 5 ## So, diameter ## = 2πr = 2*3.1416*5 = 31.42 cm ## And area of the circle ## = πr^2 = 3.1416*5^2 = 78.54 cm^2...
  37. A

    Which is harder to pull apart, a circle or a triangle?

    In deciding which shape of ring I should use to secure an anchor to an anchor trolley I came across two choices, a circular ring or a triangular ring. While either will surely work, I began to wonder which would be more difficult to pull apart. Most of the information I found is about forces...
  38. Suyash Singh

    Equations for Circles and Ellipses: A Helpful Guide

    I have no idea what to do please help me. although i did this for the second equation, x/2h+y/2k=1 this represents an elipse first equation is circle
  39. yecko

    Stress transform - Mohr's circle

    Homework Statement For the beam and loading shown below, (a) find the state of stress at point A in the Cartesian coordinate system indicated in the figure. (b) use Mohr’s circle to determine (i) the principal stress and principal plane; (ii) the normal and shearing stresses acting on a plane...
  40. O

    B Shadows in a Circle: Exploring the Direction of Sundial Shadows

    Let us say we form a circle with stick, just like a sundial. But instead of one stick in the center, we put sticks all around on the circle. Will the shadows all point in the same direction?
  41. hm_tested

    B How to find a length of a "radius" not centered in a circle?

    Generally in a circle, the radius of the circle is uniform around the circle due to it being at the center, this is the obvious part. However, let's say the the radius was shifted away from the center so that it is somewhere in the circle, in this case called r'. Given that the original radius...
  42. isukatphysics69

    Find the radius of the circle for this airplane

    Homework Statement Homework Equations f=ma v^2/r The Attempt at a Solution Σfx = FNcos(θ) = (v^2/r)*m Σfy = FNsin(θ) - mg = 0 FN = mg/sin(θ) (mg/sin(θ))*cos(θ) = (v^2/r)*m gcos(θ)*r = v^2*sin(θ) r = v^2sin(θ)/gcos(θ) v = 150m/s θ = 38 r = 1793m i have...
  43. M

    B Area of a circle without calculus

    π is defined by the ratio of the circumference (R) of a circle to its diameter. The area of the circle is πR². Can this be derived without calculus (or Archimedes method)?
  44. Monoxdifly

    MHB [ASK] Tangent of a Circle (Again)

    If the line x + my = 1 is a tangent of the circle x^2+y^2-4x+6y+8=0, the value of m is ... A. -2 B. \frac{1}{4} C. \frac{1}{4} D. 3 E. 4 Looking at the circle's equation, the center is (2, -3) and the radius is \sqrt5. If I know the coordinate where the line meet the circle I think I can solve...
  45. R

    Mohr's circle with weld across element

    Homework Statement [/B] problem - https://imgur.com/SKeTUXNHomework Equations Mohrs circle The Attempt at a Solution [/B] I have drawn 2 induced loading elements (shown at the bottom of of my working) I just seem to have conflicting information from some class examples and am wondering...
  46. R

    Homework check - Mohr's circle & Shear stress in I beam

    Homework Statement Mohrs circle question - https://imgur.com/SKeTUXN Shear stress in I beam question - https://imgur.com/34yTyCAHomework Equations Mohrs Circle - None Shear stress in I beam - I = d . b^3 / 12 tmax = (F / I . b) . (A1 . y1) + (A2 . y2)The Attempt at a Solution For the...
  47. Monoxdifly

    MHB [ASK] Tangent of a Circle

    One of the tangent line equation of the circle x^2+y^2+6x-8y+12=0 at the point whose absis is -1 is ... A. 2x - 3y - 7 = 0 B. 2x - 3y + 7 = 0 C. 2x + 3y - 5 = 0 D. 2x - 3y - 5 = 0 E. 2x - 3y + 5 = 0 By substituting x = -1, I got: (-1)^2+y^2+6(-1)+8y+12=0 1+y^2-6+8y+12=0 y^2+8y+7=0 (y + 1) (y +...
  48. Monoxdifly

    MHB Circle Equation: Solving for x^2 + y^2 + Ax + By = 0 w/y=4/3x

    A circle L is going through the point O (0, 0) and P (6, 0). The center is in the line y=\frac{4}{3}x. The equation of the circle L is ... A. x^2+y^2+6x-8y=0 B. x^2+y^2-6x-8y=0 C. x^2+y^2-8x-6y=0 D. x^2+y^2+8x+6y=0 E. x^2+y^2-4x-3y=0 Since the equation of a circle is x^2+y^2+Ax+By+C=0, I...
  49. Physiona

    Quadratic & Equation of a Circle

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  50. J

    Interpreting Dip Circle Measurements: True or Apparent Dip?

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