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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11
votes
3answers
140 views

How can the centers of these 5 related circles be specified as a formula?

This is my first time posting in this forum, so please forgive me if my question is too involved or if I've posted it in the wrong area. I hope someone finds it interesting enough to try their hand at ...
0
votes
2answers
141 views

How many sides can a polygon have before it is “considered” a circle?

Good day, my family had a dinner discussion about polygons and how many sides a polygon has in relation to the angle measurement you'll get when you measure an "arc" encompassing a "side" of the ...
0
votes
1answer
8 views

closure of dual group in pointwise convergence.

I have something which seems kind of trivial but I can't seem to prove it. Let G be an abelian topological group and let T be the circle group. Denote by G* the group of all continuous homomorphisms ...
1
vote
3answers
58 views

What is the equation of a general circle in 3-D space?

I know that $(x-x_0)^2+(y-y_0)^2-r^2=0$ is a general planar circle and $(x-x_0)^2+(y-y_0)^2+(z-z_0)^2-r^2=0$ is a general sphere. I want to know the general expression of a circle in space. Can ...
0
votes
1answer
132 views

Find the area of the shaded region

This is the Figure, $ABCD$ is a square , $AB = BC = CD = DE = 21cm$. $AC$ and $BD$ are the diagonals of the square. The two semi circles are drawn with $AD$ and $BC$ as diameter. Find total are of ...
0
votes
1answer
33 views

How to solve a ratio between radiuses of the attached diagram?

I have a red circle with a radius of 1. I'd like to get the exact ratio between it and the bigger blue circle radius. So how do you calculate AI/AJ in this case? I suppose it going to involve square ...
0
votes
2answers
46 views

Standard form of the equation of a circle : does the order matter?

The distance formula is $d = \sqrt{(x2 - x1)² + (y2 - y1)²}$ If the two points are (1, 2) (3, 4), it doesn't matter whether one write : $d = \sqrt{(1 - 3)² + (2 - 4)²}$ Or $d = \sqrt{(3 - 1)² + ...
0
votes
1answer
21 views

Polar Represantation of Shifted Disk

How to represent a shifted circle or disk (I mean the center of the circle is not at origin) in polar coordinate? For example I have a circle/disk in z-Domain like this: I thought this: $z = ...
0
votes
2answers
89 views

Geometry Problem about Circles and Tangents

It is the second problem from my maths notebooks, which is still unsolved. I translated it from Russian, so their may be some discrepancies in translation. So, I also added image. First problem was ...
0
votes
1answer
107 views

Find the Center of Tangent Circles

One of my math tests has this question. A circle has its center at $(6,7)$ and goes through $(1,4)$. Another circle is tangent at $(1,4)$ and has the same area. What are the possible ...
4
votes
1answer
45 views

Fit circle between points located on unit-sphere

Suppose I have a sphere of points with two coordinates (two angles), all points are located on a unit sphere, so radius of the sphere is one. Now my problem is, I want to find empty circles, or ...
1
vote
2answers
48 views

Find the side of the pentagon

Let $ABCDE$ be a pentagon inscribed in a circle. Given that $AB=CD$, $BC=2AB$, $AE=1$, $BE=4$, $CE=8$. Find $DE$. I am unable to use the properties of circle in this question. All I could do was fund ...
0
votes
5answers
47 views

The Equation of a Tangent Line to a Circle at a Point

How do you determine the equation of the tangent line to the circle $(x-4)^2 + (y+3)^2 = 25$ at $P(8,-6)$? Thank you in advance.
3
votes
4answers
66 views

Limit of ratio of areas of triangles defined by tangents to a circle

Let $AB $ be an arc of a circle. Tangents are drawn at $A $ and $B $ to meet at $C $. Let $M $ be the midpoint of arc $AB $. Tangent drawn at $M $ meet $AC $ and $BC $ at $D $, $E $ respectively. ...
-2
votes
1answer
63 views

Equation of a circle with a center that passes through a point [duplicate]

Write the equation of the circle with center at (-1,3) and passes through the point (2,-4).
0
votes
1answer
85 views

What is the probability of a circle sector being chosen at random?

What should I do in order to find the probability of the sector? Can you please give me the answer to this. It will really help me out if you do.
-1
votes
5answers
886 views

How do I find the area of this shaded circle?

This circle has been bugging me for a while, and I do not know how to solve it. Can someone help me find the area of the shaded circle? It would really help me.
0
votes
1answer
42 views

How small can an external angle of a circumference be if made of tangents?

Lets imagine the angle ABC where the lines AB and CB are tangents to a circumference which center is C. Lets assume that the points where the line AB touches the circumference is P and the point where ...
1
vote
3answers
522 views

How to prove the infinite number of sides in a circle?

I was in geometry class today when I came across the following formula for the external angle of a regular polygon with n sides: $$Ea = \frac{360º}{n}$$ So I thought if $$ n\rightarrow\infty $$ then ...
0
votes
2answers
29 views

Stuck on Circles question on tangents

Here the length of AO is equal to diameter of circle. AB and AC are tangents from A. The triangle ABC has to be proved equilateral. I put it in geogebra and it was indeed equilateral. I can't find ...
-1
votes
1answer
65 views

Find equations of two circles drawn through the origin which cut another circle orthogonally and touch a line

Find equations of two circles which are drawn through the origin to cut the circle $$x^2+y^2-x+3y-1=0$$ orthogonally and to touch the line $$x+2y+1=0$$. $$x^2+y^2-2ax-2by=0$$----(1) is the general ...
0
votes
1answer
43 views

How to know if a point in a circle has crossed a plane passing through the center point?

I am creating a control in .NET which computes polar coordinates based on $(x,y)$- coordinates within a panel control. Here is an image to use as a reference: When the mouse moves over the circle, ...
3
votes
1answer
146 views

Intersection of a line through two points on a unit circle with real axis

Suppose we are given two points on unit circle which are represented as complex numbers $u$, $v$. We want to show that the intersection of the line through $u$ and $v$ and the real axis is ...
0
votes
2answers
129 views

How to calculate clock-wise and anti-clockwise arc lengths between two points on a circle

I have two points with known coordinates on a circle of known position and radius. I need to calculate two things: The clockwise arc length between the two points on the circle The anti-clockwise ...
2
votes
2answers
59 views

Simplest proof that the edge of an inscribed equilateral triangle bisects the radius

Context: I am giving a short talk on the Bertrand Paradox to a mixed group, many of whom have studied mathematics at a higher level some years ago. The point of the talk is the philosophical ...
1
vote
1answer
39 views

Circle Chord Length Given other Chord

Imagine you are given circle O with two perpendicular diameters drawn inside, named AC and BD. A chord has one point on point A and is concurrent with diameter AC and the circle. The chord extends to ...
4
votes
4answers
123 views

Find the equation of a circle, given a point on it and a point where it is tangent to a given line

The given question is: Find the equation of the circle that passes through point $(-3,-4)$ and touches the line $x-y+7=0$ at the point $(-5,2).$ What I did was: Took the given points $(-5,2)$ and ...
0
votes
3answers
101 views

Squaring of the circle

From curiosity I read about enhancements of the squaring of the circle. Right now I do not see what is wrong with the following approach: Archimedes devised that the surface of a circle equals the ...
0
votes
2answers
184 views

find the point (x,y) on the unit circle that corresponds to the real number t

t=π/4 I tried to solve this problem but i dont even know where to start! i thought you had to divide the pie into 4 then put it on a number line, but when i checked my answer it was like in quadratic ...
0
votes
3answers
118 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
56 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
34 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
75 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
144 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
33 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
41 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
128 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
71 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
228 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
58 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
66 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
36 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
37 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
185 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?