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

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3
votes
1answer
443 views

Area of triangle ABC inside circle

Consider the following diagram: $AB+AD=DE$, $\angle BAD= 60$, and $AE$ is $6$. How do we find the area of the triangle $ABC$?
1
vote
1answer
167 views

find distance from point in circle to perimiter

If I have the following circle, with centre in red and a random point in the circle in blue. I know the radius ,r, length of d, and the angle p: I then create a a new green point and I know the ...
5
votes
5answers
359 views

Prove this property for an arbitrary circle

Prove that in an arbitrary circle, the point on the circle closest to the origin must lie on the extended line connecting the circle's centre and the origin.
2
votes
1answer
93 views

What does 'the forward theorem' refer to?

I have seen the following in a circle geometry proof in a Cambridge textbook: We have proven that angles at the circumference standing on the same arc of a circle are equal. The converse of this ...
1
vote
1answer
146 views

How many coordinates are necessary to determine a sphere?

Do determine a circle, you would need at least three coordinates. How many are necessary to determine a sphere?
7
votes
3answers
20k views

How do I calculate the intersection(s) of a straight line and a circle?

The basic equation for a straight line is $y = mx + b$, where $b$ is the height of the line at $x = 0$ and $m$ is the gradient. The basic equation for a circle is $(x - c)^2 + (y - d)^2 = r^2$, where ...
0
votes
3answers
299 views

Do an axis-aligned rectangle and a circle overlap?

Given a circle of radius $r$ located at $(x_c, y_c)$ and a rectangle defined by the points $(x_l, y_l), (x_l+w, y_l+h)$ is there a way to determine whether the the two overlap? The square's edges are ...
1
vote
2answers
405 views

x Points around a circle

I would like to calculate x number of points around a circle using the circle's radius/diameter. For example, if I wanted 24 equidistant points around a circle with radius 30, how could I go about ...
0
votes
2answers
194 views

Diameter of circle with n points where adjacent points are m distance apart

How do I calculate the diameter of a circle that has n evenly-spaced points on its circumference where adjacent points are m distance apart?
0
votes
3answers
90 views

Calculate incircle radius.

A circle is inscribed in a right angled triangle ABC where AC is the hypotenuse. The circle touches AC at point P. Length of AP = 2unit and CP = 4 units. What is the radius of the circle?
3
votes
1answer
131 views

Bounds for the size of a circle with a fixed number of integer points

I know that there are infinitely many rational points on the (unit) circle. I am interested in the following question: How large has the radius of a circle to be, such that there are at least $n$ ...
2
votes
2answers
2k views

Equation of sine wave around a circle

Consider a sine wave having $4$ cycles wrapped around a circle of radius 1 unit (its center needs not be the origin of a Cartesian coordinate system). Assume that the length of axis of the sine wave ...
1
vote
1answer
401 views

Relationship between the sides of inscribed polygons

In my math textbook there's a demonstration for the calculus of the circumference of a circle that involves regular polygons inscribed in the circle, but I don't get it. The book gives the following ...
12
votes
1answer
786 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 ...
12
votes
4answers
659 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 ...
21
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
496 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
504 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
137 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
128 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
269 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
315 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
144 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
522 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
96 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
648 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
1k 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
221 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
965 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
2k 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
205 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
137 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 ...
0
votes
2answers
173 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
70 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
125 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
203 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 ...
22
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
150 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
187 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
105 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
194 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
226 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
144 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
171 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
281 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
207 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 ...