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

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0
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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
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3answers
135 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 $p$ ...
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2answers
88 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
95 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 ...
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0answers
34 views

Circle Segment - Middle Point

I want to calculate the coordinates of the point which in the middle of segment area just by knowing: angle from the center of the circle($\alpha $) , the radius and coordinates for the circle's ...
0
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1answer
31 views

complex coordinates of perpendicular chords on unit circle

I am faced with the following problem.. Consider three points $A (a), B (b), C(c)$ on the unit circle $|a|= |b|= |c|=1$. Find the complex coordinates of the point $D (d)$, where $D$ also lies on the ...
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3answers
61 views

Equation of a circle using rational fractions

Why does the following equation draw a circle ? $$\left(\frac{t^4-6t^2+1}{t^4+2t^2+1},\frac{4t-4t^3}{t^4+2t^2+1}\right),|t|\le1$$ Does it draw a perfect circle, or an approximation ? On Desmos, it ...
1
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2answers
64 views

Circle tangent to two other circles

How can i find a circle that is tangent to two circles which have the same center? Specifically i'm looking for a circle that will contain the smaller circle. I know how to find the circle whose ...
0
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1answer
35 views

How to find out circumference of circle with given centres and radius is completely covered by other intersecting circles with same radius

I want to find whether the circumference of a circle with given centre and radius is completed covered by two or more circles with given centre and same radius in matlab
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1answer
64 views

Rotation of a circle over another circle

Let the circle $d$ rotates over the circle $c$. If the angle rotation to be of 0 to 360, then how many times does the circle $d$ rotate during that process? Since the total external angle is 360, I ...
2
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1answer
56 views

Subtracting equations of two circles which don't intersect

Suppose you subtract the equations of two circles that do not intersect. In doing so, you will obtain a line which is an "extraneous solution set". Is there any geometric significance to this line? ...
0
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2answers
41 views

How can I find the centre of a circle given a segment with compass and straight edge only

I need to find the centre of a circle for which I have a segment with the bisection of the chord. I know the centre must lie on the perpendicular bisector, but I need to know how far down. I need to ...
2
votes
2answers
84 views

working backwards from $\pi r^2$

I have been dipping my toes into a bit of calculus (through the better explained website), however I have become stuck on my understanding of the area of a circle. I understand that the formula for ...
1
vote
1answer
91 views

How do I find the coordinates of 10 points spaced equally on a circle?

I am not extremely good at math but I am working with computer graphics and I need to find a way to cut a circle equally in to 10 sections. To do this I need to define 10 points on the circle and my ...
2
votes
3answers
121 views

Coordinate of the excentre of a triangle

I am just wondering that how the coordinate of the excentre comes out if we know the coordinates of vertices of the triangle.
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1answer
301 views

Optimisation problem - circle and square

A piece of wire of length $20$cm is cut into $2$ parts. the first part is bent into a circle of radius $r$ in cm, the second into a square of side length $s$ in cm. a) write down an expression for ...
0
votes
1answer
30 views

How to bound the great-circle distance of two points on a sphere, only given their euclidean distance?

Suppose I have a great-circle of a sphere in $\mathbb{R}^n$, the chord length (the euclidean distance of any two points) is $L$, how can we upper bound the arc length $C$ (for any radius)? I read ...
2
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2answers
64 views

How does the circumference of the top + bottom sides of a cylinder effect our calculations when working out the surface area?

I was watching a video tutorial on khan academy, (I've included the link at the bottom), and the question states that there is a 8cm cylinder, with a radius of 4. Part of the video shows a worked ...
2
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1answer
55 views

formula to calculate number of arch with certain angel could be fixed in a circle

I'm looking looking for a formula to calculate how many arches with certain angle could be fixed around a circle or in circular formation. I want to use that formula to write a procedure for MSWlogo ...
8
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1answer
90 views

Minimum number of circles with 3 neighbors

It is possible to arrange congruent circles on the plane in such a way that no two circles overlap and each circle adjoins exactly three other circles. The picture shows an example with 16 circles. ...
0
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0answers
50 views

Exact values on unit circle

Why is it allowed to draw an equilateral triangle on the unit circle to prove the exact values for $\cos(\pi/3)$ or $\sin(\pi/3)$ for example?
3
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3answers
44 views

The locus of points $z$ which satisfy $|z - k^2c| = k|z - c|$, for $k \neq 1$, is a circle

Use algebra to prove that the locus of points z which satisfy $|z - k^2c| = k|z - c|$, for $k \neq 1$ and $c = a + bi$ any fixed complex number, is a circle centre $O$. Give the radius of the circle ...
2
votes
1answer
45 views

Circle equation solution

Hi I'm stucked with this equation while transforming it into circle equation: equation is $y+\sqrt{x-x^2} = 0$ Here is my solution: $$y+\sqrt{x-x^2} = 0$$ $$y+\sqrt{-1(x^2-x)} = 0$$ ...
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vote
3answers
265 views

The point of contact of between two circles and common tangent at this point.

A large circle and a small circle have equations $x^2+y^2+2x-4y-27=0 $ and $x^2+y^2-12x+10y+43=0$ respectively. a) Show that the two circles externally touch at a single point and find the point of ...
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2answers
134 views

Three circles having centres on the three sides of a triangle

NOTE: I would appreciate it if you provided a hint and not the whole solution. BdMO 2014 Nationals: In acute angled triangle ABC, considering a portion of side BC as diameter a circle is drawn ...
0
votes
2answers
50 views

Locus of complex number in complex plane

I have the following complex number: $G = \xi + i\eta$ $\xi = 1-\sigma(1-\cos\phi_m)$ $\eta = -\sigma\sin\phi_m$ how can I find the locus of this complex number? I am told without proof that it is ...
0
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0answers
33 views

Vector for arcs in path

I have path created from lines and arcs. I want to create next path inside or outside of this given path with given offset. For line I calculate line equation and it gives me simple perpendicular ...
2
votes
1answer
47 views

Deriving angle from sin or cos

How can I derive the value in degrees of an angle starting from either the cos or sin value? $$ \cos(t) = c_{1} \quad \text{or} \quad \sin(t) = c_{2} $$
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2answers
44 views

Intersections of two parabolas given focii

As part of Voronoi's algorithm, I need to calculate the intersection of two parabolas to compute a breakpoint at run time. I've spent literally 8 hours on this, and I've only gotten my equations to ...
3
votes
3answers
257 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
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1answer
47 views

Finding the angle value given 1 point and the centre of a circle

I got the coordinates of the center of a circle $(a,b)$ as well as one other point $(x, y)$. From those I can derive the radius by applying square root to the result of following formula. $$ (x-a)^2 ...
1
vote
1answer
124 views

Finding the points of intersection of a circle and a line

In a test (of math in arabic language) we we're asked to find the points of intersection of a circle and a line. Their equation is given. In the test I solved system of equations made of their ...
3
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0answers
57 views

A question concerning radians and arc length

I was asked by a colleague yesterday about how the formula for the arc length of a circle is derived. I wanted to give them a correct answer, so I said I'd get back to them once I'd thought about it ...
1
vote
1answer
47 views

Find part of segment between two circle centers

I drew the following image to help me explaining the question: Having two circles Source and Target, I want to build an arrow like in the image. The Source has coordinates $Source(sx, sy)$ and ...
0
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0answers
36 views

Coloring a circle

A circular spintop is colored in blue, red and green. Whenever the spintop is rotated 120 degrees, the pattern of colors looks exactly the same, only that blue becomes red, red becomes green and green ...
2
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1answer
58 views

Finding the radius of a third tangent circle

Sorry if this is a foolish question, but I'm having difficulty understanding how to solve for $r_3$ in the following diagram... According to WolframAlpha's page on tangent circles, the radius of ...
0
votes
1answer
42 views

The vertical projection of a chord of a circle?

I was wondering if anyone could help me with the problem below (finding x): So we are given t_i (the initial tangent angle to the circle), t_o (the exiting angle of the tangent of the circle), the ...
1
vote
1answer
30 views

Truncated geometric progression on the complex unit circle - how to minimize the maximum real value

Let $a = \text{e}^{i 2 \pi k}$, and let $n$ be a natural number. Then I have a set defined as follows: $S = \{ \text{Re} (a), \text{Re} ( a^2 ), \ldots, \text{Re} (a^n) \}$ I want to minimize $T = ...
0
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1answer
56 views

How do I correctly measure the circumference of a circle

I found How exactly do you measure circumference or diameter? but it was more related to how people measured circumference and diameter in old days. BUT now we have a formula, but the value of PI ...
2
votes
1answer
61 views

Requiring a Geometrical proof

In the figure, ABCD is a square circumscribing a circle ($\pi_1$) whose center is E, the point of intersection of the diagonals AC and BD. With A as center, AB as radius, sector ABD is drawn cutting ...
0
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2answers
54 views

Finding whether the quadrilateral is cyclic or not

Is a quadrilateral with sides lengths $3$, $3$, $4$, and $4$ cyclic? Progress I found that sides joining 3 and 4 are of equal length. then I found that other diagonal should also have same length ...
11
votes
1answer
153 views

Is a line just an infinitely large circle?

A line is infinite, right? Well, if $-\infty = \infty$, then a line is an infinitely large circle. (Does this have something to do with $1/0$?) It seems wrong, is it? Could I disprove it? How ...
0
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2answers
43 views

Sine on a Circle

I'm walking a quarter mile circular walking track. The width of the track is 8 feet across. If I walk from one side of the track to the other, walking a sine wave that has a 20 foot period, how much ...
0
votes
1answer
13 views

Simple Angle from X and Y Axes Input

I am trying, given the position along the $X$ and $Y$ axes from a controller, where the positions range from $-1$ to $1$ ($1$ being up on the Y and right on the X) to convert this to the direction of ...
0
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4answers
51 views

Finding the equation of a circle given one point and radius

What is the equation of the circle which passes through the point $(0,2)$ with radius $4$ and whose center lies on the line $y = x$?
0
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1answer
52 views

What is the radius of a circle tangent to two lines with a known angle between them

Given angle, $\alpha$, and distance, $d$, what is the radius, $r$, and angle, $\theta$, in the image below in terms of the known quantities?
0
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1answer
54 views

Drawing lines from tangents from two circles on both sides.

I need to draw two red lines connecting the tangents from two circles on both sides. I need an algorithm that would get them based on any angle these circles are in relation to another. I need the ...
0
votes
1answer
23 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
3
votes
3answers
71 views

Find equation of a circle

Find equation of a circle passing through $(1, 1)$ and touching the circle $$ x^2 + y^2 + 4x - 6y - 3=0 $$ at the point $(2, 3)$. I am stuck as I cannot find more than $2$ equations for $3$ unknowns. ...
1
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0answers
50 views

How to calculate the height of a segment based on radius and area

I'd like to calculate the height of a segment based on the area. I have the radius of the circle, the area of the segment and need to calculate the height of the segment. I found the following ...