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

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2answers
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Solving for $\theta$ in a circle

Let's say you have a pendulum hanging straight down and touching the ground at the lowest point. The pendulum has length $l$. If you pull the pendulum back so that the end is height $h$ above the ...
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1answer
28 views

Rules of Inscribed Angles

https://www.dropbox.com/s/chbs2vilr9wjkvz/20140819_130744.jpg Image of question found above. I don't understand why angle BCD is formed by tangent and chord and is equal to 1/2 of arc BC.
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2answers
42 views

Placing a circle in a square lattice

Two part question. Consider the square lattice $\mathbb{Z}^2$: Imagine you are going to place a circle of radius $r$ somewhere in $\mathbb{R}^2$. Question 1: What is the radius of the largest ...
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1answer
41 views

Enlarge 3 Circles about the same factor to find the Intersect

I currently have 3 circles that not intersect at all. Like this: Now i would like enlarge the circles about the same factor to find the intersection of this three circles. I have tried following ...
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0answers
36 views

Convex optimization approximation

Consider the optimization problem $\mathcal{P}_0$ $$ \min_{x \in \mathbb{R}^2} \left\| x-p \right\|^2 $$ $$ \text{sub. to: } \ A x \leq b, \ \ x_1^2 + x_2^2 = 1 $$ where $p \in \mathbb{R}^2$ is a ...
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0answers
40 views

Finding circle which touches two functions

I wasn't sure whether my issue is with my Mathematica code or the actual way I am trying to figure out my problem so if it is a Mathematica issue I can ask it on that stack exchange. Firstly I have ...
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0answers
42 views

What is the curve's name for the “reciprocal” equation of a circle?

The equation of a unit circle is $$(x-a)^2+(y-b)^2=r^2$$ When the origin $$(a, b)=(0,0)$$ the equation becomes $$y=(1-x^2)^{1/2}$$ Naturally when this equation is plotted on graph paper we get a ...
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2answers
46 views

Intersection of circle and ellipse

I'm looking for the points of intersection of a circle $x^2 + y^2 = r^2$ ($r$ is known, origin is $(0,0)$) and an ellipse $(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1$ ($a,b,x_0,y_0$ are known). ...
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1answer
47 views

Distance to the perimeter of a circle with given radius, distance traveled from origin, and direction

I am programmer by trade but am running into some trouble with a geometry problem. I basically want to start at the center of a circle, travel any distance within the radius, turn any direction, and ...
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1answer
53 views

Find area of shaded region in circle

I am working on this SAT question. Progress AD = 3 largest radius =3 second largest = 2
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2answers
21 views

Circle Line segment intersection

I have a circle with radius r and center $(c_x, c_y)$. I have a line segment $(x_1, y_1)$ and $(x_2, y_2)$ given $(x_2, y_2)$ is always a point inside the circle. I am trying to find the ...
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1answer
163 views

How to find the area of intersection of two circles using axiomatic geometry?

Problem: square(ABCD) is a regular square, and a circle touches internally in the square. Also, arc(BD) divides the square. Then calculate the area of the colored region. This question is easily ...
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0answers
31 views

Translate vertical movement into radial movement?

I've tried all sorts of things, but I'm no mathematician and I've conceded defeat. So I come here for help. I don't know if I really worded the question correctly since I don't even know what I should ...
1
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1answer
29 views

Not understanding arc midpoint computation

I'm trying to find the midpoint of an arc, so I found this page which describes the midpoint formula. I pasted the formula & description from the site below. Let origin-centered arc of radius ...
2
votes
4answers
83 views

Area of a circle sector

I have been given the following proportional relationship to derive the area of a circle's sector: $\large\frac{\text{A}}{\text{Area of the circle}}=\frac{\text{s (arc length)}}{\text{circumference ...
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1answer
33 views

Work out center of a partial circle

If I have a small section of a circle, inside a square. I know the height and the width of the square and therefore the width and height of the arc, what would be the quickest (not necessarily the ...
2
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1answer
45 views

Unit circle can't be covered by one chart

I am hoping that someone can give me a proof showing why the unit circle cannot be covered by one coordinate chart, or a reference where I can find a proof.
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1answer
38 views

Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$?

We are on $\Bbb{R}^2$. Let $A_1,\cdots,A_n$ be $n$ points on the unit circle. Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$ ? ( of course I mean the distance ...
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2answers
38 views

Deformable circle from a cubic Bezier approximation

I plan to draw approximate circles using a piecewise cubic Bezier representation. The representation should use four Beziers and be defined by four interpolating control points (let us call them ...
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4answers
54 views

Circle - finding the equation

Question: Find the equation of a circle whose center is in the first quadrant; touches the x-axis at (4,0) and makes an intercept of length 6 units on the y-axis. I am getting a faint idea where to ...
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1answer
27 views

Can any vertex of an isosceles triangle represent the centre of a circle, and the base vertices represent points on the circumference of that circle?

This question occurred to me doing this circle geometry problem, and I was wondering if anyone could clear it up. Geometrically, it seems it would make sense, provided that 2 sides are equal (equal ...
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0answers
23 views

Function where circle is special case with i=2

I saw this function some while back but cannot recall its name and therefore cannot find it and research it. Can someone please remind me its name? $|x|^i + |y|^i = 1$ where $i$ is ${1,2,3,4,5 ...}$ ...
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1answer
36 views

Outer interval of circle intersection

Is there a consistent way to calculate the outer interval $\left(~\mbox{element of}\ \left[0, 2\pi\right]~\right)$ of a circle created by an intersection ?. I calculated the intersection points and ...
2
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2answers
223 views

Finding the position of a moving point [closed]

A point is moving on a given curve. For example, curve equation is: $$x^2 + y^2 - 10y = 0,$$ which is a circle with $5$ meter radius. If point is on $(0,0)$ at $t = 0$ and is moving on the curve ...
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3answers
47 views

Finding formula for an arc of a circle that fills a rectangle

I'm working on a program where I need to draw an arc in a rectangle fulfills these requirements: 1) The arc must be part of a perfect circle (not the band!), must not be oval 2) The arc intersects ...
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2answers
23 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
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0answers
16 views

Coordinate geometry of circles; Circles through the points of intersection of 2 other circles

Here is my question. Let S=0 be the equation of circle 1 and T=0 be the equation of circle 2. There is a standard expression that, if you want the equation of a circle passing through the points of ...
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1answer
20 views

Coordinate Geometry of circles; Radical Axis question

If one of the diameters of the circle $x^2+y^2-2x-6y+6=0$ is a chord to the circle with center at $(2, 1)$, then the radius of the second circle is? Apparently the solution is $3$, with the ...
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2answers
29 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
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1answer
27 views

Minimal number of points to define a rotated ellipse?

What is the minimal number of points $N$ to uniquely define the semi-major axis $a$, the semi-minor axis $b$ and the rotation angle $\omega$ of an ellipse whose the center is known/fixed (this is ...
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1answer
43 views

Number of triangles formed by all chords between $n$ points on a circle

We have $n$ point on circumference of a circle. We draw all chords between this points. No three chords are concurrent. How many triangles exist that their apexes could be on circumference of ...
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1answer
44 views

problem about length of perpendicular chords

Question $AB$ is chord of circle $O$,points $D$ and $E$ are chosen on $AB$ in a way that $AD=BE$.prove two chords that are perpendicular to $AB$ and pass $D$ and $E$ points are equal.(prove $LK=MN$) ...
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1answer
32 views

Determining intersecting points between square and circle

I unfortunately have spent too much time trying to solve this question, and have turned to you for help. The corner of my square has intersected some circle, and I need to move it out. I only know one ...
1
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2answers
45 views

Geometry : find the points of tangency between two lines and two circles [closed]

I have a programming problem. I need to find the intersection points between two lines tangent to two circles and the circles! I have the circles' radiuses and centers. So I need points ...
0
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2answers
54 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
2
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1answer
34 views

How to embed this circle tangent to the other circles?

I want to construct a circle that would be tangent to the $3$ circles and would have its diameter lie somewhere on the segment $BI$. $EF$ includes the diameters of the $3$ given circles. $EB=BF$. ...
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3answers
27 views

The sum of the squares of the length of the chord intercepted by the line x+y=n $n$…

Problem : The sum of the squares of the length of the chord intercepted by the line x+y=n $n \in N$ on the circle $x^2+y^2=4$ is (a) 11 (b) 22 (c) 33 (d) 13 I am unable to understand this ...
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1answer
16 views

Best fit circular arc to an elliptical arc?

Is there a standard procedure or algorithm for finding the best fit circular arc to an elliptical arc ? Where the ellipse arc is: symmetrical about the minor axis, subtending [+theta, -theta] from ...
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2answers
18 views

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ the…

Problem : If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ then c +d equals (a) 60 (b) 50 (c) 40 (d) 30 Solution : Equation of common chord ...
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1answer
50 views

Circle with perpendicular chords

A blue circle is divided into $100$ arcs by $100$ red points such that the lengths of the arcs are the positive integers from $1$ to $100$ in an arbitrary order. Prove that there exists two ...
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2answers
37 views

Area of a segment

Two circles of radii 5cm and 12cm are drawn, partly overlapping as shown. Their centres are 13cm apart. Find the area common to the circles?
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1answer
41 views

Parametric equation of a circle given starting point.

Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v=0$ and you travel clockwise with a period of $3$. So, I know that I require to have a $x(v)$ and ...
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0answers
47 views

Parametric equation of a circle with given radius and starting point

Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v = 0$ and you travel clockwise with a period of $3$. So, I know that I require to have a $x(v)$ ...
2
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1answer
48 views

Diameter of inscribed circle

How can i express diameter of inscribed circle in terms of radius of three circles.
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2answers
46 views

Do the centroid of a unit n-hemisphere and that of the whole n-sphere coincide when $n \to \infty$?

It is known that the distance between the centroid and the center of a unit semicircle is $\displaystyle\frac{4}{3\pi}$, whereas that of a unit hemisphere is $\displaystyle\frac{3}{8}$. I am ...
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1answer
17 views

If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P…

Problem : If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P ( Geometric progression). Then lengths of tangents drawn to them from any point on the ...
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2answers
36 views

Find the radius

Consider the parabola $y=x^2$ and a circle which is tangent to the parabola at the points $(1,1)$ and $(-1,1)$.Find the radius of circle. My try:I write the general equation of circle ...
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1answer
110 views

Inverted Circle?

The equation I have is $$\Large x^{\frac23} + y^{\frac23} = 3^{\frac23} $$ I know what the graph looks like, but I don't know how I would find points other than the intercepts mathematically. How ...
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1answer
45 views

The point of contact between a line with a circle

My question is: I have a circle of radius 40 and a line which the circle is tangent to. So, if I take a circle of radius 80, do the two circles have the same point of contact? I mean: do they (my ...
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5answers
145 views

How to work out miles between Longitude values based on a Latitude value.

We know that when Latitude is 0, the distance between Longitude values is roughly 69 miles. When the Latitude is +/-90, Longitude values are 0 miles. At 0 Latitude, the earths circumference is ...