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

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triangle circle inside it, heights prove exercise

Point $O$ lie inside $ABC$ triangle. Points $A1,B1,C1$ are projections of $O$ on heights led from $A,B,C$ Prove that if $AA1=BB1=CC1$ then $AA1=2r$, where $r$ is radius of circle inscribed in $ABC$ ...
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2answers
27 views

Arranging identical balls in a circle

In how many ways can 4 identical red balls and two identical white balls be arranged in a circle? This is an elementary problem, but many tries have not yet yielded results. I tried by taking the ...
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1answer
28 views

Length of tendon in circle [on hold]

What is the length of chord that pass on two specific point. For example I have circle ( r=1) point1 :(x1,y1) point2(x2,y2); length of chord?
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1answer
14 views

Searching for the measure of an angle (circle)

http://gyazo.com/8e4baf0eb175628b5272751168fd47aa We know that $\widehat{ACB}=75^\circ$ and that $\left(AB\right)//\left(CD\right)$. We know that $\widehat{CDB}=35^\circ$, and $A, B, C, D$ are on a ...
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0answers
10 views

Find the Langitude and Longitude of the centre point of a circle given a point on the circumference.

I couldn't find a similar question! Given I have the latitude and longitude (x,y) of a point on the circumference of a circle, and I want the circumference to be 1000m. An example of a lat lang I ...
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1answer
9 views

Angle between a line and a circle that it goes though

I just solved a task regarding the angle under which a certain line goes through a circle. The line naturally has two common points with the circle. It seems that the angle between them is the same in ...
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1answer
23 views

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
32 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
29 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
28 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
38 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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32 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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8answers
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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
53 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 ...
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1answer
62 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
41 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
24 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
33 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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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
18 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
56 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
27 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 ...
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2answers
72 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
77 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
27 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 ...
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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 ...
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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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109 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 ...
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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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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
99 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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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 ...