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Questions tagged [circle]

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

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3answers
34 views

How do I find the radius/diameter of a circle, when given the perimeter? [on hold]

I have had a question about this, and my math teacher did a wretched job teaching this. Does any of you know how to find the radius/diameter of a circle when given the perimeter?
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0answers
17 views

Optimal covering with $n$ non-necessarily equal discs

What kind of algorithm can I use to search for an optimal (minimum area) covering of a limited region of the 2d plane with $n$ discs $(x_i, y_i, r_i)$? I've found many investigations on fixed radius ...
2
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1answer
47 views

Prove the equality of circle's areas

Through a random point inside the circle, we draw $4$ lines with $45$ degrees between each other. Prove, that the total area of odd pieces, equals total area of even pieces. I suppose there is a ...
3
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4answers
241 views

Equilateral triangle on a concentric circle

Is my idea correct? 3 concentric circles of radius 1, 2 and 3 are given. An equilateral triangle is formed having its vertices lie on the side of the three concentric circles. What is the length of ...
0
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1answer
26 views

Angle of a Star Inscribed in a Circle

I don't even know where to start on this: In the figure, point O is the center of the circle, points A, B, C, D and E all lie on the circle, and both segment AD and CE go through point O. Angle BEC ...
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0answers
52 views
+100

For any orientation-preserving circle homeomorphism $f$ with rational rotation number , $\Omega(f) = Per(f)$

Here's a problem that I've been unable to solve, even though I've tried. Let $f: \mathbb{S}^{1} \to \mathbb{S}^{1}$ be an orientation-preserving circle homeomorphism with rational rotation number. ...
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0answers
15 views

Computational geometry relationship between 2 arcs

I'm writing a program which is making offsets for provided shapes. On the attached picture you can see example of my arc object and all known values. Let's assume that a direction is CW. $O$ - ...
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1answer
38 views

What is the radius of the semicircle?

Diagram : a 40cm wire bent to make a closed figure that consists a rectangle and a semicircle. (Kinda like a door with a curved top) Total perimeter of diagram / length of bent wire (rectangle + ...
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2answers
43 views

Is there a closed-form solution for tangent circle in lens of two other circles?

I am given real values $p, s, t, u$ and wish to find unknown values $r, v$. As shown in the diagram below, $p$ and $s$ are radii of two given circles, with centers at $(0,-p)$ and $(0,t)$. At ...
1
vote
0answers
23 views

Circle can always represented as $\{z:|z-c|=k|z-d|\}$

I am reading Howie's Complex Analysis. There I see this remark: The observation that $c$ and $d$ are inverse points is the key to showing that every circle can be represented as $\{z:|z-c|=k|z-d|\}$...
5
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2answers
114 views

Geometry high school math competition question

Let $ABC$ be an equilateral triangle with side length $2$. Let the circle with diameter AB be $\gamma$. Consider the two tangents from $C$ to $\gamma$, and let the tangency point closer to $A$ be $...
3
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0answers
27 views

Kind of hard(?) geometry proof [duplicate]

I am struggling with this proof. Consider the circle $\Gamma$ with a diameter $AB$. Another circle $\Lambda$ is drawn such that it is internally tangent to the $\Gamma$ and tangent to the diameter $AB$...
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1answer
22 views

Proving that a point P is on a circle and a line

Given a circle $C$ with center $A$ and radius $r$. Given a line $D$ with a vector ${u}$ passing through point $P_0$. Knowing that $P$ is on $D$ only if $P = P_0 + t u$ Knowing that $P$ is on $C$ if $\...
1
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1answer
32 views

Find the Length of $QP$

Given two circles with radii $8$ and $6$ units with centers $A$ and $B$ such that $AB=12$ If $P$ is mid point of $QR$ Find Length of $QP$ My try: I assumed $A(0,0)$ and $B(12,0)$ So the equations ...
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0answers
31 views

Find a parametric equation that draws a quarter circle of radius 9 that crosses the y-axis and is as much in quadrant III as it is in quadrant IV.

In preparation for my precalculus test, I was assigned many challenge problems, including this one. I have been struggling to find a solution to this question, as when I graphed my solution, it seemed ...
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1answer
27 views

Rectangle trapezoid

I would be very grateful if you can help me with this problem. I've constructed the median ON, N ∈ BC, and I was able to find that the triangle OCN is isosceles (height and median coincide). Probably ...
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0answers
21 views

Definition of constant-curvature curve embedded on an Ellipsoid of revolution

I am interested in identifying a type of curve so I can do literature review on it. What is the name of a curve embedded on an ellipsoid of revolution in which the curvature of the embedded curve is ...
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2answers
28 views

Area of shaded portion inside a circle. [closed]

How do you find the area of orange shaded region given the inner diameter of the green circle is $14\sqrt{2}$ units?
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0answers
39 views

Gauss Circle problem upper bound derivation

On this page, http://mathworld.wolfram.com/CircleLatticePoints.html It says that |E(R)|<2sqrt(2)piR, how did Gauss show this?
7
votes
2answers
154 views

Given $n$ circles of radii $r_1,r_2,…,r_n$ inseparable by straight lines, prove that they can be covered by a circle of radius $r_1+r_2+…+r_n$

Definition: A subset $A\subset\mathbb R^2$ is inseparable by straight lines if there doesn't exist a straight line $L$ such that $L \cap A=\emptyset$ and $L$ divides $A$ into $2$ nonempty parts, ...
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2answers
45 views

Circle in which side of square is given [closed]

I am not Able to proceed with this question .
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1answer
48 views

Drawing a figure in advanced geometry.

I was not able to draw figure for a question. Question was From a point of intersection of two circles, the lines to the centers of similitude bisect the angles between the radii of the circles. ...
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1answer
42 views

How do you find the area under a circle using definite integrals

I am studying calculus, and am wondering how to take a definite integral under the area of a circle. As a circle is $x^2 + y^2 = r^2$, how do you perform integration with a y in your formula? My ...
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1answer
44 views

Solve the equation $R^{2}\frac{\arccos(\frac{h}{R})+\frac{h}{R}}{2} = \pi r^{2}$ for $R$

I have the following equation and I want to solve for $R$. $$R^{2} \left( \frac{\arccos \left(\frac{h}{R}\right) + \frac{h}{R}}{2} \right) = \pi r^{2}$$
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1answer
59 views

How to find the radius of the circle after adding the area of segment?

I am making a game where a circle can hit a wall an interact with it to simulate a ball hitting a wall. When the circle is 1/4 the radius through the wall the area of the part in the wall will be ...
1
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3answers
37 views

Movement of $1/z$ in complex plane

How is moving $\frac{1}{z}$ in complex plane if $z$ is described by a circle which has radius $r$ and center $a+b*i$ I've just started complex algebra and still having some trouble imagining it. How ...
6
votes
3answers
107 views

Circle problem in which i wanted to find value of $PQ$

Find a value of $PQ$: Let the radius of bigger circle be $R$, and that of the smaller circles be $r_1$ and $r_2$. Hence we can find value of $R = 10$. I don't know how to proceed further to find ...
0
votes
3answers
30 views

How would I go about graphing $2x+3 > x^2 + y^2$? [closed]

How would I go about graphing this problem?
2
votes
0answers
23 views

Find value of $\frac{\sum AA_1 \cos\left(\frac{A}{2}\right)}{\sum \sin A}$

Triangle $\Delta ABC$ is inscribed in a circle of radius one unit. If the internal angle bisectors of angles $\angle A, \angle B,\angle C$ meets the circle at the points $A_1,B_1,C_1$ respectively. ...
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0answers
33 views

Finding the radius of incircle of $\triangle ABC$ where each of three other circles is mutually tangent to two sides of the triangle respectively [duplicate]

In acute angled $\triangle ABC$, considering a portion of side $BC$ as diameter, a circle is drawn whose radius is 18 units and it touches two sides $AB$ and $AC$ respectively. Similarly, considering ...
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1answer
19 views

Length of a tangent segment to the vertex of the circumscribed angle

Problem statement: $AB$ is the diameter of circle $O$ with a radius of $12$. $P$ is a point on $AB$ between the center point $O$ and $B$ such that $PB = 8$. Find a) the length of the shortest chord ...
2
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1answer
140 views

IMC 2011 question involving six tangent circles

Two circles $A$ and $B$, both with radius $1$, touch each other externally. Four circles $P$, $Q$, $R$, and $S$, all with the same radius $r$, are such that $P$ touches $A$, $B$, $Q$, $S$ externally; $...
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2answers
37 views

Graphing a Circle that Doesn't Intersect the Pole

I am trying to graph a circle using a polar equation that does not intersect the pole. For example the rectangular equation would be $(x-3)^2+(y+2)^2=1$ If I use the usual way to transform this into ...
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2answers
35 views

Perpendicular distance from chord to circle

I need to find the perpendicular distance from a chord to the circle, at arbitrary distance along the chord. I found an approximation using versine, but is there an exact formula? Thanks Kevin
6
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2answers
99 views

Finding lengths when circles and squares tangents. [closed]

Should one approach by coordinates or by euclidean geometry? By pure geometry, I am not able to solve.
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2answers
47 views

Finding the distance from the flat surface to the point of tangency between two circles with having radii $2$ and $10$ respectively

I have had trouble with this problem lately. Question: Assume there are two circle with radii $2$ and $10$. The both circle are tangent to each other and are on a flat surface. Find the distance ...
1
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1answer
46 views

Intersection of Circle and Parabola

Q) Suppose the circle with equation $x^{2} + y^{2} + 2fx + 2gy + c = 0$ cuts the parabola $y^{2} = 4ax,(a> 0)$ at four distinct points. If $d$ denotes the sum of the ordinates of these four points, ...
0
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2answers
49 views

Are curves just portions of connected circles of different radii? [closed]

I just had the question in my mind, can any curve be reduced to different portions of circumferences of circles with different radii, for example the curve of $\sin$ and $\cos$, and the curve of $y = ...
0
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2answers
35 views

Help identifying the function

I plotted some raw data and it looks like it's almost a perfect circle (the first half of it). From point H till point F we can see a nice circular curve. What's the relationship between H and F? In ...
3
votes
1answer
67 views

Calculating “hypotenuses” of acute triangles in a circular segment

I have a sector of a circle split into 16 equal segments. I am trying to calculate the "hypotenuses" of the triangles formed by 2 intersecting straight lines (for example, triangle $LEQ$), which sort ...
0
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2answers
29 views

Proving that connecting $n$ points on a circle's circumfrence leads to (at most) $\binom{n}{4}$ intersections.

I ask this question in reference to the question asked here. The answers included the solution $\binom{n}{4}$ to the question of how many intersection points there are if you connect $n$ points on a ...
1
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1answer
65 views

Find the equation of the circle between 2 tangent lines

Find the radius of the circle and its position from origin. Given - equations of tangents of the circle and point of intersection of the tangents.(It's like a pair of tangents from a circle ...
2
votes
1answer
84 views

Brocard's theorem - $O$ is orthocenter of $\Delta EFI$

Consider $ABCD$ is cyclic quadrilateral, the intersection of $AD$ and $CB$ is $E$, $AB$, $CD$ is $F$; $AC$ and $BD$ is $I$. Prove that $O$ is orthocenter of $\Delta EFI$. Firstly, i will prove $OI\...
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2answers
30 views

What is the LCM of a and b if $(a+2 \sqrt{2} )/b$ is the ration of the area of larger circle and smaller circles?

Radius of all four smaller circles is $R$. If the ratio between the area of the larger circle and the sum of areas of the smallest circles is $(a+2 \sqrt{2} )/b$ then find the LCM of $a$ and $b$. ...
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3answers
75 views

Geometrical problem on semi-circles

Given that $AE$ is the tangent to the small semi-circle at $D$ and that arc $CD$ : arc $DB$ = $3 : 10$, find arc $AE$ : arc $EB$. How do I go about solving this? I do not know how to start.
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0answers
27 views

polar graphing, supposed range is between $0$ to $\pi,$ but graph drawn range from $-\pi/2$ to $\pi/2$

I'm currently studying "area bound by polar curves" on khan academy, and below is one of the question I have encountered I am puzzled by part $2$ of the official solution. I can't seem to figure out ...
0
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2answers
37 views

If there is a point on a chord of a circle, which point on the minor arc would make the length between the the two points the smallest? [duplicate]

If segment mn is a diameter of a circle f, and v is a fixed point on mn, for which point E on MN is the length FE minimized?
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1answer
17 views

Equation of circle with minimum radius that can be drawn through the points $A$ and $B.$

The line $y=mx+c$ cuts the given circle $x^2+y^2=a^2$ at two distinct points $A$ and $B.$ Equation of circle having minimum radius that can be drawn through the points $A$ and $B.$ I have approached ...
0
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1answer
66 views

Let gh be a chord of a circle ω which is not a diameter, and let A be a fixed point on gh

Let segment gh be a chord of a circle ω which is not a diameter, and let n be a fixed point on gh. For which point b on arc gh is the length n minimized?