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

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12
votes
1answer
858 views

A geometry problem seeking for proof

Circle $\odot O_1$ is tangent with circle $\odot O_2$ at $P$. Two tangent lines $AE$ and $AF$ of circle $\odot O_2$ meets circle $O_1$ at $B$, $G$ and $C$, $H$, respectively. $D$ is the in-center of ...
14
votes
6answers
749 views

Why do we use the Euclidean metric on $\mathbb{R}^2$?

On the train home, I thought I would try to prove $\pi$ is irrational. I needed a definition, so I used: $\pi$ is the area of the unit circle. But what is a circle? A circle is the set of tuples ...
22
votes
2answers
2k views

Divide circle into 9 pieces of equal area

I'd like to divide a unit circle disk into nine parts of equal area, using circle arcs as delimiting lines. The whole setup should be symmetric under the symmetry group of the square, i.e. 4 mirror ...
0
votes
2answers
576 views

Problem with finding the equations of the lines tangent to a certain circle

This is a long question, and might seem like a repost of my earlier questions, but it isn't, hear me out: In my book is written: The equation of the line tangent to the circle $x^2+y^2=r^2$ in the ...
0
votes
5answers
671 views

Find the equation of a circle which intersects another circle perpendicularly

'Find the equation of the circle with its center at $M(4,3)$ which intersects the circle $(x-3)^2+y^2=5$ perpendicularly' How can 2 circles have a perpendicular intersection, is this even possible? ...
0
votes
1answer
170 views

Put this equation of a circle in its standard form

$ x^2 + y^2 = 4x+4$ How to put it in the standard form: $(x-a)^2 + (y-b)^2 = r^2$
0
votes
1answer
132 views

Question about units and area of a circle?

Andrea is preparing an installation manual for a cell-phone tower to be used in a European country. The tower specifications are in imperial units, and she must convert them to SI for their client. ...
1
vote
1answer
303 views

dividing an offset circle into triangles

First of all - I am sorry if it is the wrong forum or if this is a very trivial question. I am not a mathematician nor a trigonometry genius - and therefor I would ask a simple answer that someone ...
0
votes
1answer
1k views

Find the equation of a circle given the radius and center (with vector length notation)

I want to find the equation but use vector length notation and I'm not sure about how to write it. $$ a) r = 2, A(-1; 1)$$ the line I'm not sure - $$|[x-x_0 , y-y_0]|^2 = r^2$$ then I do $$(x+1)^2 + ...
1
vote
2answers
330 views

Circle in the complex plane

Show analytically (finding the centre and radius) that $z(t)=\frac{1}{(1-i)^{-1}-t}=\frac{2}{1+i-2t}$ where $z(t)\in C $, that $z(t)$ traces out a circle in the complex plane as $t$ is varied.
0
votes
1answer
157 views

How to find the point of collision between an irregular shape (built out of 3 circles) and a line

I'm making a program in which many weird shapes are drawn onto a canvas. Right now i'm trying to implement the last, and possebly hardest, one. In this particular shape i need a way to find the ...
1
vote
2answers
643 views

Calculate average angle after crossing 360 degrees

For a piece of code I am writing to smooth out movements I need to calculate the average angle over the past 5 recorded angles given (used to give directionality to an object) This can be achieved ...
6
votes
1answer
110 views

What is wrong with this circle's area problem?

My solution and my book's solution don't match. Is something wrong with the my solution? If so, where and why? My book says: The radius r of a circle increases by 50%. In terms of r, what is ...
8
votes
4answers
719 views

inverting a cone to a torus

I'm looking at "A Geometric Paradox" by B. H. Brown, in the May--June 1923 issue of The American Mathematical Monthly, pages 193--195. I think people studied advanced Euclidean geometry a lot more ...
0
votes
1answer
2k views

calculating the radius of a circle if the distance between two points and the angle from the center are known

In a problem I'm working on, I have the following situation: On a circle with an unknown radius, there are two lines from the center to the edge of the circle. The angle between these lines is known, ...
2
votes
1answer
232 views

Mathematical name for the horn shape

I am looking for the technical name for the horn shape which is created by repeating circles while increasing the radius size varying with an exponential function. Any references that can help me find ...
0
votes
3answers
1k views

How to calculate radius of flush arch between two intersecting lines?

I am trying to make a corner of a robot I am designing flush for aesthetic reasons as well as safety reasons but I'm not sure how to make the arch of the corner lay flush with the two lines that make ...
0
votes
1answer
3k views

How many triangles can be formed from N points on a circle?

I have a circle with N points on it, and I want to determine how many triangles can be formed using these points. How can I do this? Thanks! Andrew
1
vote
3answers
2k views

Dividing circle into six equal parts and know the coordinates of each diving point …

I have a circle who center(0,0) and radius(100) is known. That circle is divided into 6 equal parts. I want to know the coordinates of all six points on the circle that divides it into 6 parts. Can ...
1
vote
2answers
224 views

coordinates of the point where 2 tangents to a circle cross

I have a circle of radius r. Given two lines tangent to the circle at points (x1,y1) and (x2,y2), What are the coordinates of the point where the two tangents cross?
2
votes
1answer
153 views

What are the subsets of the unit circle that can be the points in which a power series is convergent?

Let $A\subset\Bbb C$ be a subset of the unit circle. Consider the following condition on $A$. Cond. There exists a sequence $\{a_i\}_{i=1}^\infty$ of complex numbers such that $$\sum_{n=1}^\infty ...
84
votes
17answers
14k views

How do you find the center of a circle with a pencil and a book?

Given a circle on a paper, and a pencil and a book. Can you find the center of the circle with the pencil and the book?
0
votes
2answers
183 views

How to calculate arc length

I forgot my secondary school maths, so I need to ask to confirm. Arc Length = Radius*(Angle In Radian) Is it correct?
1
vote
1answer
71 views

How to prove that the following trace is a circle

$$\Gamma = { B\over e^{j\theta} -A}$$ Both $A$ and $B$ are complex numbers. The tedious way of course is to expand $A$, $B$ and $e^{j\theta}$, formulate the function into the form of $\Gamma = x + ...
5
votes
1answer
127 views

A rope and Pi's irrationality

Here is a question which has been puzzling me for some time. You have a thin rope of an integer length $L$. You can bend it to create a rectangle of perimeter $L$. Fine so far. Next, through some ...
2
votes
1answer
225 views

Angle of first circle where it intersects second circle

First, some background. I'm writing an application which a bit more mathematically challenging than what I'm used to. I have two circles that overlap (not just touch, I mean there are two intersect ...
23
votes
5answers
1k views

Trying to understand why circle area is not $2 \pi r^2$

I understand the reasoning behind $\pi r^2$ for a circle area however I'd like to know what is wrong with the reasoning below: The area of a square is like a line, the height (one dimension, length) ...
2
votes
1answer
170 views

Drawing a circle tangent to a given circle and its origin is on y-axis

I am facing a problem and I do not know if it is solvable or not. Suppose I have 2 points and a distance, $P_1$, $P_2$ and $D_x$ respectively. I need a mathematical way to find the center of a ...
1
vote
1answer
220 views

Length bisection from circular arc

I am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am ...
0
votes
1answer
117 views

Find the intersection between point and circle

given a line segment with endpoints P1 and P2 and a Circle with Center C and Radius R where it is known that P1 lies outside the circle and P2 lies inside the circle, what is an efficient way to find ...
2
votes
4answers
195 views

Quickest way to find a point on a circumference

Given the image below, A is the centre of the circle, B is a point on the circumference and AC and DB lie on parallel lines. Knowing A, C, D and the radius of the circumference, I need to find the ...
2
votes
1answer
250 views

calculated reflected point within circle

The problem to solve is this. Imagine a circle. We know two points on the circumference, anchor A and anchor B, they could be anywhere on the circumference of the circle. Draw a line between these ...
1
vote
1answer
164 views

Straightedge Only Construction of Tangents to Circle

Currently, there exists a question regarding straightedge only constructions; however, my specific question pertains something that is not found in that thread, and I do not think it will be answered ...
3
votes
1answer
177 views

What does Spivak want me to do?

This goes on in Chapter 8, on least upper bounds and related topics. I have proven $(a),(b),(c)$. The sketch is. $(a)$ If $\{a_n\}$ is a sequence of positive terms such that $$a_{n+1}\leq a_n/2$$ ...
0
votes
2answers
55 views

Problem with a circumference

I have the following equation for a circumference: $$9 X^2 + 25 Y^2 - 36 X - 50 Y = 154.$$ So far I only used this general equation: $X^2 + Y^2 + A X + B Y + C = 0$, but now $X^2$ and $Y^2$ are not ...
-3
votes
9answers
285 views

Why is $y + x = 3$ not the same as $y^2 + x^2 = 9$

I know this is impossible, but why is the following not possible: $y + x = 3$ is the same as $y^2 + x^2 = 9$ They're meant to be equivalent.
0
votes
1answer
1k views

Find arc center from tangent lines and 'rounding value'

Simple and common question: I want to round two intersecting lines with arc, so I need to know its center point. I have defined: AP - first line BP - second line |PR| - rounding scalar value, so ...
1
vote
2answers
238 views

Calculating circumference from 2d coords

I'm trying to calculate the circumference of a circle given say three reference points from a 2d coordinates that would form an arc. The problem is the reference points may be slightly inaccurate so ...
1
vote
1answer
2k views

Find the center of circle given two tangent lines and two points

Probably simple to solve but I'm a bit stuck. I am given two lines that are tangent to a circle and the circle must go through $P_1$ (which is the end of Line 1) and $P_2$ (which is the end of Line ...
41
votes
4answers
3k views

Do circles divide the plane into more regions than lines?

In this post it is mentioned that $n$ straight lines can divide the plane into a maximum number of $(n^{2}+n+2)/2$ different regions. What happens if we use circles instead of lines? That is, what ...
2
votes
1answer
156 views

How to constrain disks that intersection of them is inside unit circle

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ ...
1
vote
1answer
340 views

A question about circle geometry

Three points $A$, $B$ and $C$ are on a circle, $G$. Suppose $\overline{AB}>\overline{AC}$. Let $M$ be the midpoint of the arc of the circle containing the points A and N the point in $AB$ such ...
0
votes
2answers
84 views

How do I get get x and y position of a particular location on two intersecting circles (Vesica Pisces)?

I have the radius and center $(x,y)$ on both circles, but how do I get the $(x,y)$ of the red circle, or in other words how do I get the $(x,y)$ position of where the circles intersect at the top or ...
0
votes
1answer
94 views

Minimal rotation to avoid collision of circles

The discriminant of a certain quadratic equation which determines when two circles (hyperspheres?) will collide, provided they travel with a constant velocity is $$(\Delta v\cdot\Delta s)^2-(\Delta ...
0
votes
1answer
176 views

Geometry for Middle for schoolers (joining 5 points on a circle)

If there are five points on a circle. How many line segments can be drawn on it, but without overlapping the regions?
0
votes
2answers
1k views

2 concentric circles, inner circle has a tangent, relations between those points

AB is tangent to the inner circle, consider the trigonometric circle. Knowing the radius of both circles, is there a relation between those 2 point's coordinates ? Their coordinate being $A = (R ...
26
votes
13answers
29k views

Calculus proof for the area of a circle

I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$ and it struck me as being particularly easy. The only ...
0
votes
1answer
150 views

Making a logo with processing, can't figure out a coordinate…

I'm struggling to make a simple logo, I have no deep knowledge of Inkscape so I'm doing it with a little bit of processing. The problem is I can't figure out how to determine one certain point's ...
1
vote
3answers
1k views

Difference Between Degrees on a circle

What kind of math would I use to calculate the difference between two degrees on a circle? Say, 38 and 272 degrees? When I just subtract one position from another sometimes it's more than 180 or ...
0
votes
2answers
5k views

How do you find an angle between two points on the edge of a circle?

I have a two points on the circle surface and I also know the center of the circle. I want to calculate the angle between those two points which are on the circle surface. Is this formula is suitable ...