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

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find arclength given angle of circle in degrees and radius oif circle

I'm having a lot of difficulty with getting this to make sense and the answer in the book is just '8.4 in' Q " You want to make an 80 degree angle by marking an arc oin the perimeter of a 12-in. ...
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0answers
17 views

How to determine the length of an equilateral triangle from its inradius?

An equilateral triangle is drawn with inradius 3cm. How can one find the length of a side of the triangle?
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0answers
13 views

Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
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2answers
25 views

Find intersection points of a line with a circle, and the equation of another circle passing through those points [on hold]

If the line $x=2y$ meets the circle $x^2+y^2-8x+6y-15=0$ at points $P,Q$, find the co-ordinates of $P$ and $Q$ and the equation of the circle passing through $P,Q$ and at the point $(1,1)$. Could I ...
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3answers
22 views

Find coordinates of point that intersects circle

I got a circle of 900 radius, knowing its center coordinates A(x1, y1) and got another point with also known coordinates B(x2, y2). I draw a line between point A and B. It intersects the circle in a ...
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1answer
25 views

Circle in the plane of complex numbers

Let $K = \{z \in \mathbb{C}: |z−a|=r \}$ be a circle in $ℂ$. Show that, for the case that $|a|$ is not equal to r, the image of $K$ under the transformation $z$ $\to$ $\frac {1}{z}$ is a circle too. ...
10
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1answer
337 views

The number of the circles which are tangent to two circles and to a line

Suppose that we have two distinct circles and a line on a plane and that the distance between the centers of the circles is bigger than the sum of their radiuses. Also, suppose that the two circles ...
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1answer
61 views

Triangle, Circle Problem

What is the area $\triangle DEF$ ? I solved it using analityc geometry. I want to see if there is way to solve it using plane geometry. I did it: $x^2+y^2=400$ $(x+10)^2+y^2=100$ I found the ...
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0answers
13 views

Circumcentre of three points X, Y, Z, given distance from each to points A and B

I'm racking my brain trying to figure out where to start on this, and it's been too many years since working on these kinds of problems. I have six measurements which I'd like to use to calculate a ...
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1answer
31 views

equation draws a circle in C

It be $a\in\Bbb C , b ∈\Bbb R$ and $|a|^2 > b$. Also, $a'$ is the conjugation of $a: a' = x - iy$ when $a = x + iy$ (and equally for $z$). It needs to be shown, that the solutions of the equation: ...
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1answer
18 views

Two body problem (rotation around a fixed central point)

Is there a way which isn't physics related, but just using pure maths to find the solution to the following problem: If i have two lines of different lengths at t=0 overlapping each other. They are ...
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1answer
15 views

Calculate point P(x,y) in a circle given a radius and angle degree

I'm doing a program in Java to draw a PieChart based on given value as link below. data for piechart Given that the diameter, radius, angle degree, center point (150,150) and First Point A (150,0) ...
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2answers
33 views

How Do We Find Points On A Circle Equidistant from each other?

I'm a programmer and I saw this question on stackoverflow which exactly does my job: http://stackoverflow.com/questions/13608186/trying-to-plot-coordinates-around-the-edge-of-a-circle. In this, the ...
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1answer
28 views

Time based algorithm to make object orbit another in electron-type path?

I'm positioning an object in 3d space, and I want to make it orbit another object, in a semi-random electron-like orbit, such that it always stays the same distance from the origin. I can make it move ...
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0answers
19 views

How to calculate the fundamental group of $S^3$ without two linked cirles

I need to find: the fundamental group of the space obtained by cutting out the three-dimensional $S^3$ sphere of two circles, once linked with each other. Can you help me? I have no idea about it, i ...
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2answers
30 views

Need help finding algorithm to fix specified problem

First I want to say that I am not a mathematician, so asking a question in this area is not easy for me. So I will describe the issue in my words which is not the nice way. So this is what I do: I ...
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0answers
14 views

Prove three chords of a circle are concurrent iff their poles with respect to a circle are collinear.

This probably would be a very simple problem if I could use any theorem I wanted about poles and polars, but in the book they give a definition and they say the problem should be solved using only ...
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1answer
23 views

Geometry - Cyclic Quadrilaterals

Three points A,B,C lie on the circumference of the circle, with center as O. If angle(ACB) = 115 deg. Need to find angle (BOC)? Please post your approach?
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1answer
48 views

Geometry - prove, that the center of circumscribed circle of a triangle lays on line.

Inside the angle, which vertice is the point $M$, the randomly selected point $A$ is drawn. From this point the ball is released, which at first reflected from one side of the angle at point $B$, ...
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1answer
23 views

Plane-geometry problem with circles and tangents

I have a problem that even my smartest colleagues were able to solve. This is to get the radius of the smallest circle in the drawing below. Using a computer program, I managed to get that lightning ...
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7answers
240 views

area of figure in sector of intersecting circles

I need to find an area of blue part of figure APBC. I draw line segments between B and C, between C and A, and got equilateral triangle. I'm stuck here. Please help. Thanks. |AB| = a, P is midpoint ...
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1answer
30 views

Simple circle question

let AB be diameter of circle and AC be the chord. Let a tangent is drawn from C to meet AB produced at D.If BAC=30,Prove that BC= BD SOLUTION ACB= 90 ABC=60 CBD=120 After that I am confused
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1answer
46 views

How to calculate the range of angles at which a line will intersect a growing circle? Arc length?

I am working on some simulation software in which I have an entity (e) that is spiralling around a particular point (p). As e continues to move around p, the radius of the circle that it is following ...
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1answer
30 views

Is any property of orthocenter related in this question?

While practicing mathematics Olympiad questions , i got the below given question . Though the solution is given , I am not able to bypass certain steps ... Can anyone please explain me why angle KPA ...
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5answers
108 views

What kind of curve is made of half circles?

I have this curve. It's definitely no sine or cosine. It consists of half circles. How do you call it and how do you describe it mathematically?
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2answers
28 views

Equation of circle through three given points.

Yes, there are many methods to find the equation; the easiest being the process of solving the eqn. of circle putting the three points. But what I didn't understand is the another method which my book ...
2
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1answer
17 views

convex quadrilaterals and circles

Suppose you have an arbitrary convex quadrilateral call it $WXYZ$ and four circles with diameters $WX, XY, YZ, ZW$. How would you prove that the four circles would cover the whole quadrilateral ...
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2answers
26 views

Center of a circle from two chords.

If two chords of a circle intersect and are $\perp$ to each other, is it possible to find the distance from the intersection point of the chords to the center? I was trying to use the power of a ...
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2answers
58 views

Coordinates of the intersection of two tangents to a circle

Let $A = (x_A, y_A)$ and $B = (x_B, y_B)$. Let $\gamma$ be a circumference of radius $r$, centered in $(0, 0)$; $A$ and $B$ lie outside of $\gamma$, and on the same side of some line $L$ through the ...
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1answer
48 views

Place three circles such that they uniquely intersect at each point in the plane

Is it possible to place three circle centers in a plane such that there is a single unique three-way intersection between the three circles for any given set of circle radii? For example, see the ...
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2answers
22 views

How far to move a circle along a ray so that it intersects with another circle only once?

Given two 2d circles that have intersected at two points, how do I find the distance along a ray that passes through the center of one of the circles so that when that circle is translated along that ...
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0answers
23 views

Slopes of equally spaced lines

This is an incredibly simple question, I'm sure, but I'm only in 7th grade and can't quite riddle it out. Say you wanted to lay out equally spaced points about the circumference of a certain circle, ...
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0answers
8 views

Rotate a point on circle by an angle such that the point attains a new coordinate axis.

I have this circle with known radius and centre w.r.t to both new and old coordinate axes given by NBase and Base respectively. I need to find a point P and Theta such that when vector OP is rotated ...
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1answer
28 views

Finding functions in Inscribed Triangle

If we have a circle of radius $R$ around center $O$ and its inscribed triangle $XYZ$ that is acute as well as scalene. $XY$ is the longest side. $XA,YB, ZC$ are the altitudes of the triangle $XYZ$. ...
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0answers
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question about the formulae of the circle

I don't speak English very well but I am asking this because I could not find the answer that I want in my country's website. The question is that if the coordinate of the center of a circle is ...
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1answer
21 views

Equations for different quadrants of a circle

In the circle $x^2$ + $y^2$ = $a^2$, what's the general equation for the arcs in each of the quadrants?
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1answer
15 views

Distance between center of side of regular polygon inscribed in a circle, and the perimeter of that circle?

Point A : The center of a side of a polygon inscribed in a circle Point B : The point on the perimeter of that circle that is opposite Point A I want to calculate the distance between Point A & ...
2
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2answers
110 views

circular reasoning in proving $\frac{\sin x}x\to1,x\to0$

The classic proof for $\frac{\sin x}x\to1,x\to0$ is using a squeezing theorem based on arguments about areas of circles. But as far as I know, all deduction of formula of circles' area is based on ...
2
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1answer
18 views

Graphing Circles, Ellipses, Parabolas, and Hyperbolas

I need help plotting a curve on a graph where the distance from focus1 is always the same ratio to the distance from focus2. For instance, lets assume focus1 is -5 along the x axis, and focus2 is +5 ...
0
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1answer
37 views

Calculate distance in x,y from center based on distance and degrees.

I'm terribly sorry if this question is written like a 5-year old.. But that's the level I'm on in terms of math and coordinate calculations. (Just realized I don't even know what to tag this question ...
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1answer
68 views

Finding circle with two points on it and a tangent from one of the points

Two points P1(x1,y1) and P2(x2,y2) are known. In addition, a line slope passing through P1 is known. The aim is to construct a circle (or circular arc) that it passes through both P1 and P2 and it is ...
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1answer
70 views

Differentiation of a circle

As a discus thrower is spinning counterclockwise to throw a discus, the discus travels along the path given by the circle $x^2+y^2=4$. If the discus is released at the point $(\sqrt2,\sqrt2)$ and ...
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0answers
24 views

What is the sum of the interior angle of a circle?

There is a convenient formula for deriving the sum of the interior angle of polygons which is $$180^\circ\cdot (n-2)$$. By building the limit it seems that for a circle the value is infinite. But it ...
2
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1answer
27 views

In every polygon circumscribed about a circle, there exist three sides that can form a triangle.

How can one show that in every polygon circumscribed about a circle, there exist three sides that can form a triangle? (This was posted by another user and then deleted while I was typing my answer.) ...
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2answers
87 views

Number of ways to seat people around a circular table

I got (i) which is $9!$, but there are no answers for the second question. I stated that $$P(\text{none together})=1-P(\text{3 together})-P(\text{2 together})$$ and got the answer $7/12$. Is this ...
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0answers
25 views

find points on circle in 3D pace perpendicular to line

I'm working with 3D image data and have little algebraic knowledge. I have an 3D image whit each pixel divined by its x,y,z position. What I need is to get the values of all pixels on a circle inside ...
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5answers
254 views

How can I find the radius of a circle from a chord and a section of the radius?

Draw a circle with center O. Line AD is a chord that is 8cm long. The arc above is smaller than the one below. B is the center of AD. Line CB is a line that is 2cm long. It meets AD at 90°. ...
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1answer
29 views

Computing overlapping circle positions, equidistant from each other.

Hello, I am a programmer and I wanted to develop an application that would have several overlapping circles in the same location, where each circle can be selectable. Is there a mathematical way of ...
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0answers
22 views

Find the minimum radius of the circle which is orthogonal to two given circles

Problem : Find the minimum radius of the circle which is orthogonal to both the circles $x^2+y^2-12x+35=0$ and $x^2+y^2+4x+3=0$ . Solution : Let the equations : $x^2+y^2-12x+35=0.....(i)$ and ...
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3answers
20 views

Cyclic quadrilaterals - finding the size of an angle

I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question ...