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

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12
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4answers
2k views

Is it possible to divide a circle into $7$ equal “pizza slices” (using geometrical methods)?

Or is it possible to divide a circle into n equal "pizza slices" (I don't know how to call these parts, but I think you'll know what I mean), where n hasn't got a common divider with $360$? Or are the ...
1
vote
1answer
249 views

How to prove that a circle passing through the center of the circle of inversion invert to a line?

link to the referenced picture: http://www.flickr.com/photos/90803347@N03/9220374271/ In order to prove the Arbelos Theorem, as in the picture above, one need to prove that the semicircle $C$ invert ...
1
vote
2answers
433 views

Maximum Distance between points on circle

What is the greatest possible distance between two points: one on a circle with radius 1 and centre (1; 2) and the other on a circle with radius 2 and centre (4; 6) I am not familiar with the ...
1
vote
2answers
75 views

Points on a circle

36 points are marked, equally spaced, on the circumference of a circle. Some of the points are marked with crosses in such a way that the distances between every two consecutive crosses are all di ...
0
votes
0answers
139 views

Compute multiple Rectangles area intersect by a circle

I've a need to compute the area of single elements (dice) of a matrix like this: http://i.stack.imgur.com/EKVSz.jpg The matrix is composed by 'c' columns and 'r' rows and every element/rectangle has ...
3
votes
1answer
1k views

Determining the angle degree of an arc in ellipse?

Is it possible to determine the angle in degree of an arc in ellipse by knowing the arc length, ellipse semi-major and semi-minor axis ? If I have an arc length at the first quarter of an ellipse and ...
0
votes
2answers
54 views

Finding a point on a circle

I have a circle that I am trying to find series of points on. I know the radius and horizontal tangent point at the top of the circle. I need to find a point that lies on the circle's circumference ...
1
vote
1answer
52 views

Sectors of a Circle

I am programatically drawing sectors of a circle with radius 55 on a cartesian plane which runs from -55 to 55 on the x and y axes. I would like the first sector to be drawn at 0,55. I know I can ...
0
votes
1answer
86 views

Calculate x,y line terminiating point of section of a circle

I have a Cartesian plane running from -41 to 41 on the x and y axes and a circle centered on 0,0 with a radius of 41 divided up into a number of sections of different areas. I know the percentage ...
4
votes
2answers
389 views

Applonius Circle/ Ford Circle / Infinite GP / Circle Packing

All the smaller circles are mutually tangent and continue to infinity. What is sum of radii of all the smaller circles?
6
votes
3answers
15k views

How to determine the arc length of ellipse?

I want to determine the arc length of a ellipse. So what data should I know ? And what law should I use ? For example I have this ellipse on picture below: How can I determine the $d$ length of ...
1
vote
0answers
91 views

Circle in a simplex

Let $T$ be a $2$-dimensional simplex in $\mathbb{R}^2$. A circle $C(x,y,r) \subset \mathbb{R}^2$ is given by its center $(x,y) \in \mathbb{R}^2$ and radius $r\ge 0$. Show that the set of circles in ...
1
vote
0answers
105 views

Circle Geometry and Conic Section textbook

I seek a textbook for good conic section and circle geometry questions. Slightly above introductory level. - slightly. But I wouldn't mind introductory level questions to consolidate my knowledge. I ...
1
vote
1answer
761 views

How to calculate the inverse of a point with respect to a circle?

The theory said: The inverse of a point $P$, with respect to a circle centered at $O$ and has a radius $r$, is the point $P'$ such that The three points $O$, $P$ and $P'$ are colinear. $OP \times ...
3
votes
1answer
122 views

Find coordinates of intersection between two circles, where one circle is centered on the other

I'm writing a program where an object needs to move from point A to point B. A and B are points on the same circle. Point B corresponds to the intersection between the circle and another circle ...
0
votes
1answer
83 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...
1
vote
3answers
27 views

If $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$

I would appreciate if somebody could help me with the following problem Q: if $\overline{OQ}\times\overline{OP}=r^2 $ then $\angle OAP=\frac{\pi}{2}$ ($r$: radius of $C$, $C$: circle, $O$: ...
0
votes
2answers
56 views

Proof Error? A line-segment of a circle is a metric.

In O'searcoid, Metric Spaces, he provides the following example of a metric space: Suppose C is a circle and, for each $a,b ∈ C$, define $d(a,b)$ to be the distance along the line segment from $a$ ...
1
vote
1answer
450 views

Collision between a circle and a rectangle

I am trying to create a simple model for collisions between a circle and a rectangle to be used in a computer game. The reason I am asking this question here rather than stack overflow is that the ...
1
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2answers
639 views

What is the area of the shaded region of the square?

To find area of shaded portion in the below figure, the picture generate by following mathematica code. ...
0
votes
1answer
103 views

Tangent of circumscribed circle

I found a solution online which it said : "It's easy noted that $AG.AE$ = $AD^2$ = $AF^2$ (Using tangent of circumscribed circle)" I found this not obvious at all. I know that $AD = AF$ but why it ...
1
vote
2answers
323 views

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral?

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral? I gather it doesn't because most of the proofs I've seen use derivatives etc. If ...
0
votes
1answer
331 views

How to Find the First Moment of Area of a Circular Segment by Integration

Given a segment of circle symmetric about the $y$-axis, I'm wondering how to apply the integral $Q_x = \int y \, dA $ to find the first moment of area with respect to the $x$-axis. I'm having ...
1
vote
3answers
1k views

Triangle inscribed in circle, vertex at circle's center, solve for unknown angles.

$O$ is the center of the circle , $A$ and $B$ lie on the circle what are the possible values of $x$ and $y$ I found answers options , asked to mark one or more ...
0
votes
2answers
30 views

What is the ratio of the perimeter of $OPRQ$ to the perimeter of $OPSQ$?

Area of circle $O$ is $64\pi$. What is ratio of the perimeter of $OPRQ$ to that of $OPSQ$ ($\pi = 3$)? Okay i have tried couple of things but seems its not working . Please suggest me proper ...
1
vote
0answers
81 views

Probability of a certain circular configuration

Pick each of $n$ angles , $\theta_1$ through $\theta_n$ , uniformly randomly in the range $[0,2\pi$]. Define the distance $d_{i,j}$ between $\theta_i$ and $\theta_j$ by $d_{i,j} = \min(|\theta_j - ...
1
vote
1answer
2k views

Is there an equation to find the intersection of 3 circles without complex steps?

Is there a way to find the intersection 3 circles without substituting and solving the equations into each other? The reason is because I am making a trilateration program, so I won't really be able ...
0
votes
3answers
8k views

Find the equation of a circle given two points and a line that passes through its center

Find the equation of the circle that passes through the points $(0,2)$ and $(6,6)$. Its center is on the line $x-y =1$.
3
votes
1answer
387 views

Do the tangents of two circles define concentric circles?

Given two non-overlapping circles, $R_1$ and $R_2$. The radii of $R_1$ and $R_2$ may be different. The distance between the centers of $R_1$ and $R_2$ is defined as $x$. Draw the four tangents ...
0
votes
0answers
43 views

Zero cell formed by connecting n random points on a circle by chords

To start, think of a regular n-gon inscribed in a circle. If the vertices of the n-gon are all connected by drawing cords between the other vertices, then another smaller n-gon is created at the ...
1
vote
2answers
159 views

Simple question about circumference of circle

Q: The physical education teacher asked to one classroom, by vote, choose a sport between volleyball, basketball and football, to practice in class the following week. pie chart: The segment AB, ...
2
votes
1answer
322 views

Find the area of a circle that is NOT covered by the rectangle

Using the following image for a visual: Is there a formula or equation I can use to find the area of the circle NOT overlapped with the rectangle (i.e. the filled in orange part)? I know all of the ...
1
vote
2answers
125 views

Optimum fitting for flanges in a rectangular plate

I have a $2500~\text{mm}\times6300~\text{mm}\times25~\text{mm}$ (width $\times$ length $\times$ thickness) steel plate I want to cut flanges of diameter $235~\text{mm}$ can anyone please suggest $1)$ ...
6
votes
2answers
168 views

Circle Chord Sequence

This is my first post, so be nice! When I was in my first Geometry class in high school, I asked the teacher the following: Given a circle of radius 2a, find the length of the chord running parallel ...
1
vote
1answer
265 views

Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
2
votes
4answers
217 views

Proof of three points are enough to draw one and only one circle

Using the circle theorems or otherwise, I explained why the process locates the centre of the arc. However, I do not know what 'accuracy limitations of this technique' means. I don't think there is ...
5
votes
4answers
2k views

Newbie: determine if line *segment* intersects circle

I've read related posts, including: How to tell if a line segment intersects with a circle? where the suggestions are probably relevant, but above my level, and the final solution is actually not ...
1
vote
2answers
138 views

Determine counterclockwise moving

in my app, I let user touch and move to draw an arc. After drawing, I got a set of points. Is there any way to determine that user draw the arc counterclockwise or reverse counter clock wise?
2
votes
1answer
1k views

What is the area of the shaded part of the circle?

In the diagram below, line segment $AT$ is a diameter of the circle with center $O$. What is the area of the shaded part of the circle? $AT= 16$. Half of the circles area is equal to $100.48$, on ...
1
vote
0answers
169 views

family of circles in bipolar coordinate system

I don't get the idea how the equation for this family of curve is $\displaystyle y^2 + (x - a \coth v)^2 = \frac{a^2}{\sinh ^2v}$ from this article on Wikipedia. Suppose, the equation is ...
0
votes
1answer
158 views

Drawing a triangle in a unit circle

This is a question that I derived for a long time ago. It asks if we draw a triangle in a unit circle does all arc lengths $(\alpha ,\beta ,\theta)$ and sides of triangle $(a,b,c)$ can be rational ...
1
vote
3answers
7k views

Determine center of circle if radius and 2 tangent line segments are given

Given the radius and its $2$ tangent lines and their point of intersection of a circle. A similar question is How to calculate the two tangent points to a circle with radius R from two lines given ...
11
votes
6answers
20k views

Area of intersection between two circles

Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres ...
2
votes
1answer
1k views

A unique circle with 3 points proof

I have prove the theorem: There is only one circle passing through three given non-collinear points in both geometrical and algebraic ways. THere is one question that I just have no idea with. 'the ...
12
votes
1answer
2k views

A hard geometry problem on circles

I found this problem on a website and I couldn't do anything. Do you have any ideas, hints? Edit: If I say $$\frac { { \partial }^{ 2 }f }{ \partial { a }^{ 2 } } +\frac { { \partial }^{ 2 }f }{ ...
3
votes
2answers
92 views

Two questions on clock arithmetic

I have two questions on clock arithmetic, both of which I have solved, but I am looking for neater proofs. Let us suppose we have a circle named $\mathbb{Z}_n$ with $n$ equally spaced points on it ...
1
vote
0answers
101 views

Is there a continuous version of $tan^{-1}(\frac{y}{x})$ for the entire unit circle?

The fact that $tan^{-1}(\frac{y}{x})$ only "works" for the upper-right quadrant makes some calculations (for a physics simulator) impossible. I of course use $atan2(y,x)$ in the code, that's not what ...
6
votes
1answer
92 views

Area of circles: represent $x$ in terms of $r_1$ and $r_2$

See the image. Area of green and red regions are equal. Can you represent $x=|O_2D|$ in terms of $r_1$ and $r_2$ for $r_1> r_2$ ? Edit: The point $O_1$ does not enter in the region of small ...
1
vote
1answer
536 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
0
votes
2answers
61 views

Calculate Point based on distance in 2D-Space

I have a Point P in unit circle (on or in it) with a radius of r. How can I calculate a Point Q with a fixed radius of x, which has the same angle like P