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

learn more… | top users | synonyms

0
votes
3answers
109 views

length of arch by startpoint endpoint and center of arch

I have a software that draws arches. What I need is to calculate the arch length (actual lenght of the line) by knowing only these informations: x,y coordinates of startpoint of the arch x,y ...
2
votes
4answers
48 views

What is the angle of a line that is tangent to a circle and passes through an arbitrary point?

I made this illustration to clarify the question: How would I find the angle of this line relative to the bottom line? If the boxes have length x instead of 1, what is the generic solution?
2
votes
1answer
54 views

Express a Line as a Circle with infinite radius

I have see a few proofs that, in some systems, a circle with infinite radius is a straight line. A nice example of this is stereographic projection in the complex plane. I have also see simple proofs ...
2
votes
1answer
32 views

Line with predefined length tangent to circle

I have one math problem which I'm trying to solve. I know it could be done but I'm a little bit "rusty" with my algebra. I'm kindly asking for help. Problem and procedure of my solution are shown in ...
0
votes
1answer
65 views

Translate 2D point to 3D coordinate system

I have a bunch of points in a 3D coordinate system that approximates a circle. I'm able to find the best-fitting plane of the points, and then find a 2D coordinate system in that plane, using the ...
0
votes
0answers
44 views

Can the radius be solved with just this information?

All the information that I have is that the arc starts at 357.5° which is 6mm from the outer possible reach. Is it possible to calculate the radius of the circle with this information.
2
votes
3answers
126 views

Find radius of fixed length arc of a circle in a bounding box when the circle intersects the edge of the bounding box

I have a bounding box that is represented as a Cartesian starting point $(0,0)$ with a width and a height. I have a circle with centre point that can be anywhere within the bounding box. The ...
0
votes
0answers
32 views

area of a sprinkeler.

A rectangular lawn has an area of 677 square meters. Surrounding the lawn is a flower border 4 meters wide. The border alone has an area of 548 square meters. A circular sprinkler is installed in the ...
0
votes
1answer
36 views

Scale position points in a circle.Look like normal scaling

I have an Art degree, no math involved, so sometimes when doing 3D graphics and envisioning problems, it's hard to search for solutions over the internet since I don't have good pointers for search ...
1
vote
2answers
111 views

Parametric equation of an arc with given radius and two points

so I need the parametric equation of the arc. So, arc is a sector of a circle. Parametric circle equation is: $$ c \equiv f(t) = (\cos(t), \sin(t)),\quad 0\le t < 2\pi $$ So, we just need to find ...
1
vote
2answers
60 views

I need to prove that this line is a tangent to the circle

The problem is this: Given two different points, $A$ and $B$, take the midpoint between them ($O$) draw the circumference $\Gamma (O,OA)$ Take any point $C$ on $AB$ and draw a line $t$ perpendicular ...
0
votes
1answer
59 views

Divergence (or second derivative) of circle

The circle has the uniform shape because a second derivative is 1. That is an intuitive guess - the line turns around at constant rate (i.e. the first derivative changes at constant rate), which means ...
7
votes
5answers
226 views

How to find the center of the circle that contains three given complex numbers?

Suppose $\alpha_1, \alpha_2, \alpha_3 $ are complex numbers which are not collinear. Is it possible to use some geometry to find the center of the circle that contains $\alpha_1, \alpha_2, \alpha_3 $ ...
1
vote
1answer
56 views

Goat on a leash problem

I have a problem with next data: I have a grass meadow with the shape of circle, and its radius is "r" I have a goat on a leash. I need to know length of a leash and how far pale, where leash is ...
2
votes
2answers
52 views

Finding integer solutions

Find all integer solutions to the problem $y^2+x^2-6x=0$. How I solved this was to complete the square then finding the coordinates: $(0,0), (6,0), (3,3), (3,-3)$. What I would like to know is there ...
0
votes
0answers
14 views

Locating point using 4 point data

currently I have 4 points of data on a circle, each point at a delta of 90 degrees. Like so: Now using this data I would like to locate point(s) on the circle depending on the size of the numbers. For ...
1
vote
1answer
35 views

How to calculate angle

Given that radius is $7'$ and that tile width is $12''$, how many tiles are needed to close the full circle, when distance between each tile is $1/4''$, and at what angle does each tile need to be cut ...
1
vote
3answers
34 views

Finding circle of a sphere through two points

We have two points $P_1, P_2$ on a sphere $S$ of radius $R$. Suppose for $r \ll R$, the distance between $P_1$ and $P_2$ is less than $2r$. Then, $P_1$ and $P_2$ both lie on exactly two radius-$r$ ...
0
votes
1answer
48 views

Widest part of a sector

Coordinates of the center of a circle, radius, initial and final angles of a sector are given. How to find coordinates of the endpoints of a segment (A and B) connecting borders of sector in its ...
2
votes
6answers
166 views

How do we define arc length?

In trying to write a nice proof of the derivatives of $\sin(x)$ and $\cos(x)$, I encountered a serious problem, namely that I have never seen a proper definition of the notion of arc length. Based on ...
0
votes
1answer
39 views

Cos, Sin, Tan or another?

I have this circle, and I want to find the lengths of the two green lines. Heres the situation: How do I calculate that?
0
votes
1answer
32 views

Calculate the radius knowing arcs' length

I have a problem where I know the length of 2 arcs of concentric circles (which are R and r) and I also know the length between the 2 circles which is l in my drawing. Any idea how I can find the ...
47
votes
17answers
10k views

Why is a circle 1-dimensional?

In the textbook I am reading, it says a dimension is the number of independent parameters needed to specify a point. In order to make a circle, you need two points to specify the $x$ and $y$ position ...
0
votes
1answer
32 views

How to solve this task about circles and lines intercepting each other?

We have drawn some lines and circles on a paper. Every two has an interception, but none three goes through the same point. How many lines and circles have we drawn if we have 75 interceptions?
0
votes
1answer
336 views

Area of a square inscribed in a circle of radius r, if area of the square inscribed in the semicircle is given.

If a square is inscribed in a semicircle of radius r and the square has an area of 8 square units, find the area of a square inscribed in a circle of radius r. I started by assuming that the side of ...
4
votes
3answers
393 views

Find the length of the chord given that the circle's diameter and the subtended angle

A chord of a circle subtends an angle of 89 degrees at its centre. Find the length of the chord given that the circle's diameter is 11.4 cm. The problem I have here is that I can't visualise this ...
1
vote
1answer
120 views

Finding an angle on a triangle inscribed in a circle

EDIT: It appears as though the text has made a typo. The angle should be $\theta - \phi$. !! How is angle $\angle OBW_2$ calculated in terms of $\theta$ or $\phi$ if the only angle measures given are ...
7
votes
2answers
87 views

'3-point' curve

If you have a loop of string, a fixed point and a pencil, and stretch the string as much as possible, you draw a circle. With 2 fixed points you draw an ellipse. What do you draw with 3 fixed points?
1
vote
1answer
36 views

triangle circle inside it, heights prove exercise

Point $O$ lie inside $ABC$ triangle. Points $A1,B1,C1$ are projections of $O$ on heights led from $A,B,C$ Prove that if $AA1=BB1=CC1$ then $AA1=2r$, where $r$ is radius of circle inscribed in $ABC$ ...
0
votes
2answers
94 views

Arranging identical balls in a circle

In how many ways can 4 identical red balls and two identical white balls be arranged in a circle? This is an elementary problem, but many tries have not yet yielded results. I tried by taking the ...
0
votes
1answer
52 views

Length of tendon in circle [closed]

What is the length of chord that pass on two specific point. For example I have circle ( r=1) point1 :(x1,y1) point2(x2,y2); length of chord?
0
votes
1answer
23 views

Searching for the measure of an angle (circle)

We know that $\widehat{ACB}=75^\circ$ and that $\left(AB\right)//\left(CD\right)$. We know that $\widehat{CDB}=35^\circ$, and $A, B, C, D$ are on a circle $C$, wich has for center $O$ (not on the ...
2
votes
0answers
46 views

Find the Langitude and Longitude of the centre point of a circle given a point on the circumference.

I couldn't find a similar question! Given I have the latitude and longitude (x,y) of a point on the circumference of a circle, and I want the circumference to be 1000m. An example of a lat lang I ...
0
votes
1answer
13 views

Angle between a line and a circle that it goes though

I just solved a task regarding the angle under which a certain line goes through a circle. The line naturally has two common points with the circle. It seems that the angle between them is the same in ...
1
vote
1answer
100 views

Perspective projection of a circle: what is the size of the semi-major axis?

It can be proven that the perspective projection (or camera projection) of a circle is an ellipse. But I also need to prove that the semi-major axis has the same size as the radius of the original ...
0
votes
1answer
40 views

Geometry: Circle inscribed in square

A circle is inscribed in a square $ABCD$ of side length $2$. There is a point $P$ on the circle such that $PA=a$. Is it possible to find $PB,PC,PD$ in terms of $a$? I haven't solved a problem like ...
0
votes
2answers
87 views

find the minimum distance between a point and border of a circle

I have a circle with radius $R$ and center $(x,y)$ and I have the coordinate of a point; I want to find the minimum path between this point and the border of circle. Here is a picture of what I said: ...
1
vote
3answers
51 views

Translate a point on a circumference

If I have a point $A$ on the circumference of a circle with origin $O$ and radius $r$, how would I find the coordinates of point $B$, which is also on that circumference, but is $d$ units away from ...
0
votes
2answers
60 views

Circle equation

Definition of problem: Write the circle equation which touches the coordinate axis and cross the point $M(2,1).$ I'm confused because I'm used to solve problems with given center but in this ...
26
votes
8answers
5k views

How to find center of a circle from only an arbitary arc of that circle

How to find the center of a circle with given an arbitrary arc. we only have the arc nothing else. Is there any known equation or way to complete the circle.
0
votes
0answers
37 views

What is the probability of shooting a puck overlapping the boundaries to get a prize?

Hello, I am new to the forum, and the maths teacher just asked the whole class this question about probability and all of us can't answer it. The question is: there are 9 grid squares on the table, ...
2
votes
3answers
62 views

Rewrite a circle's equation to easily see centre and radius

$$x^{2}+y^{2}-5x-15y+30=0$$ I'm supposed to rewrite this equation so that you can easily see the centre and radius of the circle. I don't even know where to start. According to Mathematica the centre ...
3
votes
1answer
92 views

Prove that the intersection of $BM$ and $CN$ is on the circumcircle of triangle $ABC.$

Let $P$ and $Q$ be on segment $BC$ of an acute triangle $ABC$ such that $\angle PAB$ = $\angle BCA$ and $\angle CAQ = \angle ABC$.Let $M$ and $N$ be the points on $AP$ and $AQ$, respectively, such ...
2
votes
2answers
47 views

What is the equation for this wave?

So it would be hard to describe it, it's better to see it yourself: http://physics.info/waves/surface-wave.html (Angular velocity of rotating points is constant I presume) What is it called? What ...
0
votes
2answers
41 views

Equation of circle orthogonal with $2$ given circles

Find the minimum radius of a circle which is orthogonal with both the circles: $C_1: x²+y²-12x+35=0$ and $C_2: x²+y²+4x+3=0$. I know about the condition for a circle to be orthogonal to a given ...
1
vote
2answers
38 views

Circles- finding radii of smallest and largest circle

If $r_1$ and $r_2$ are the radii of smallest and largest circle which passes through $(5,6)$ and touches the circle $(x-2)^2+y^2=4$. Then $r_1r_2$ = ??
0
votes
1answer
26 views

Question regarding characters and point open topology

I was wondering why the following claim is correct: Let G* be the group of all continuous homomorphisms from the topological group G and the unit circle (call it T). Then G* is an intersection of a ...
8
votes
3answers
193 views

Minimal circle containing set of points

Suppose that there are $n$ points in the plane $x_1, x_2, \dots x_n$, and $C$ is the minimal circle (the circle with the minimal radius) that contains all of them. If there is another point $p$ ...
0
votes
2answers
109 views

Complex number - locus of a point

Question: If argument of $\frac{z - z_1}{z-z_2}$ is $\pi\over4$, find the locus of $z$. $$z_1 = 2 + 3i$$$$z_2 = 6 + 9i$$ Approach: I tried to solve the equation using diagram, basically ...
4
votes
1answer
109 views

Nine-point circle equivalent for tetrahedrons?

Nine-point circle for a triangle is defined as the circle that passes through: the midpoint of each side the foot of each altitude the midpoint of the line segment from each vertex to the ...