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

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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 ...
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3answers
30 views

How to find the radius [on hold]

I have to find the radius of the circle. AB=1,5 AD=2 AD is a tangent Please help!
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1answer
27 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 ...
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2answers
24 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: ...
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3answers
36 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 ...
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28 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 ...
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6answers
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+100

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.
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30 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, ...
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1answer
31 views

Existence of a cyclic polygon with same sides as a given polygon [closed]

Show that for any given polygon, there exists a cyclic polygon with the same side lengths in the same order, and this polygon is unique.
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3answers
48 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 ...
2
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1answer
56 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 ...
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2answers
40 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 ...
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2answers
22 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 ...
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2answers
32 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 $r_1r_2$ = ??
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1answer
25 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 ...
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0answers
15 views

Calculate the area on a sphere of the intersection of a spherical cap and a great circle

Given a sphere of radius R with a spherical cap on it defined by the radius r, and a great circle intersection the spherical cap on the sphere. What is the area of intersection of the spherical cap ...
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2answers
44 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 ...
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0answers
27 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(alfa) , the radius and coordinates for the circle's center ...
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1answer
15 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
55 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 ...
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1answer
45 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 ...
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1answer
24 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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2answers
32 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
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2answers
71 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 ...
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1answer
75 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 ...
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3answers
75 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
31 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 ...
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1answer
20 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 ...
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2answers
26 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
44 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
85 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. ...
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45 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?
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3answers
41 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 ...
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1answer
38 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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3answers
107 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
24 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 ...
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0answers
26 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
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1answer
44 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
32 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 ...
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3answers
94 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
37 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 ...
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1answer
103 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 ...
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0answers
49 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 ...
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1answer
37 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 ...
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34 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 ...
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1answer
47 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 ...
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1answer
26 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 ...
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1answer
21 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 = ...
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1answer
34 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 ...
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1answer
46 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 ...