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

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0answers
12 views

Find ArcLength given a set of circle parameters.

I need an equation to help define a 3D curve, given starting vector, ending vector, starting point, and vertical distance between start and end points. The curve should be a segment of a circle ...
1
vote
1answer
22 views

Finding coordinates of the third point of a triangle from given?

In ABC triangle we know the coordinates of A and B vertices. We also know lengths of 2 edges shown in the picture and the third edge is calculatable. What is the most efficient functon to find x3 and ...
1
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2answers
30 views

Circular measure

Hi everyone, This is a question from a June 1984 cambridge past paper. I'm getting stuck with the part (c) and the 'hence show...' Please someone can help, I'd be very grateful.
1
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1answer
47 views

Prove that $\int_0^x \ 1/\sqrt{1-x^2} dx$ is equal to length of unit circle arc?

How to prove that $\int_0^x \ 1/\sqrt{1-x^2} dx$ is equal to length of unit circle arc? I know that the integral is $\arcsin(x)+c$ but really do not see how this is related to arc length.
1
vote
1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
8
votes
1answer
94 views

Characterization of the circle within metric spaces

There are various characterizations of the circle. To be precise, there is not the circle. There are several categories which contain an object we refer to as "the circle". In $\mathsf{Top}$ the ...
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0answers
15 views

Find The MidPoint Coordinates Of An Arc Given The Following [on hold]

Coordinates of arc starting point, arc ending point, center of arc, plus values of starting angle, ending angle, sagitta, chord, and radius. Givens: Arc is entirely within the first quadrant. Arc ...
-4
votes
1answer
24 views

Help with precalc homework | circles and radians [on hold]

Hi everyone, i need help with my homework, ive been trying to find out the answers for the last 2 questions but ended up with nothing, please help.
1
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0answers
26 views

Circle Geometry

How do you derive the equation of a circle $(x−a)^2+(y−b)^2=r^2$ if a point on the y-axis is chosen as then you cannot form a triangle and as a result not apply Pythagoras' theorem and derive the ...
1
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3answers
47 views

Proving algebraic equations with circle theorems

I got as far as stating that OBP=90˚ (as angle between tangent and radius is always 90˚), and thus CBO=90˚- 2x. CBO=OCB as they are bases in a isosceles. COB=180-90-2x-90-2x. But after this, i am ...
0
votes
0answers
35 views

Probability density function for distance between two points.

Two points are chosen randomly inside a circle (and even on the circumference) with radius $r$ What is the probability density function of the distance between the points? I would be very grateful.
0
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2answers
31 views

Highschool Geometry: Finding Common Tangent

I can't seem to identify what the arrows are indicating in this question, obviously the two lines are parallel but what does it mean? I don't know where to begin. Any suggestions?
2
votes
1answer
50 views

Intersection of two circular arcs with same center [closed]

How do you programmatically get intersection points of 2 circles given the same centers, radii, and sweep angle? The 2 circles are not exactly one whole circle. I have an equation for each circle: ...
0
votes
2answers
37 views

Calculating if a point is within the overlap of two circles

Two circles of equal radius (R) intersect as shown below. Assuming more points are uniformly distributed in an area with dimensions D*D, where D = 4*R. What is the probability that a point will be ...
0
votes
1answer
18 views

Terminals and co-terminals for angles

I'm trying to understand how my teacher converted these angles. I'm not sure if my title is correct but I'm assuming that's what he was doing. For a unit circle he had, \begin{align*} u & = ...
0
votes
0answers
23 views

Topological entropy of circle homeomorphism is zero. True or false?

may I know if it is true that $\ f: S^1 \to S^1$ a homeomorphism, then $h_{top}(f) = 0$, where $h_{top}$ stands for topological entropy. I believe this statement is true, but I cannot prove it.
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votes
1answer
43 views

Finding where $\sin(3x) = 0$. I get the concept but not how to show it. [closed]

So I'm working on a function that simplifies to $$ \sin (3x) = \pm \frac{\sqrt{3}}{2}$$ and I'm trying to find all points where this function equals $0$. I'm looking at the unit circle here, and I ...
1
vote
1answer
55 views

Algorithm - Circle Overlapping

Say you have a shape you want to fill up with circles, where by the circles overlap just enough to cover the whole surface area of the shape. The circles will remain as a fixed size however the shape ...
-5
votes
0answers
21 views

applied math - want tangent of citcle plus cnc approximation [closed]

The outline of a tear drop trailer (google instructable teardrop trailer) has a partial circle in its side view outline. The leading edge is rounded to reduce wind resistance and improve esthetics. I ...
0
votes
0answers
14 views

How do we sketch the ellipse determined by $T(\vec{x})$ and determine its axes, given an expansion factor?

I have been told that if $\left\{\exists \, T(\vec{x})^{-1}\mid T(\vec{x})=A\vec{x} \mid \mathbb{R}^2\mapsto\mathbb{R^2}\right\}$, then the image $T(\Omega)$ of the unit circle $\Omega$ is an ellipse. ...
5
votes
1answer
42 views

Fitting a circle

Given a figure like , how can I determine the radius of the circle with middlepoint H analytically? CDFE is a square with sides 6/5, with E and F being points on the circles with radii 2.
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0answers
41 views

Help with this coordinate geometry question involving cirlces and parabolas.

Question: A point $P$ in a plane moves such that it remains at a fixed distance $r$ from a fixed point $A\equiv(r,r)$. (i) Find the equation of the locus of point $P$ (in terms of $r$). Another ...
0
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0answers
24 views

How to get points of lines tangent to 2 circles

How do you get the points of lines tangent to two circles, where both starting point and end point of line are exactly touching their respective circles? Please help. Thanks
2
votes
2answers
31 views

How to calculate radius of a spherical surface having four circles touching one another?

There are four circles having radii $r_1, r_2, r_3 $ and $r_4$ touching one another on a spherical surface of radius $R$ (as shown in the picture below, four colored circles touching one another at 6 ...
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votes
0answers
23 views

Arc subtended by inner infinitesimal angle

I am trying to find the length of the bolded arc: Assume $\theta$ is infinitesimally small, $r_A$ is the distance from the point of intersection of the chords to the point of contact of the tangent ...
1
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1answer
25 views

Find point inside circle but outside of n- other circles

There is one green circle and 0 to n red circle(s). I'm trying to find a point inside the green circle, but outside all red ...
1
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1answer
62 views

Find circumcenter when distance between ABC points of triangle with two points's ratio given

The complete problem is: I am having three points A,B,C whose ratio of the distances from points (1,0) and (-1,0) is 1:3 each. Then I need the coordinates of the circumcenter of the triangle formed ...
1
vote
1answer
67 views

What are the distances from a line to the tangents of a circle?

I have a line given by two points, and a circle given by its origin and radius. I need to find the perpendicular distance between the line and the two tangents of the circle that are parallel to the ...
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0answers
29 views

External Cirlces [duplicate]

For two circles (with centres $(a_1,b_1),(a_2,b_2)$ and radius $r_1,r_2$ respectively) touching externally and the tangent at their common point passing through the origin, I have shown that $(a_1^2 ...
0
votes
2answers
18 views

Interpolate/Increment Vector Rotation

For my 2D physics engine, I'm using the unit vectors of the direction an object is facing to represent its orientation; essentially, [Cos(theta),Sin(theta)] where theta is the object's rotation in ...
0
votes
1answer
20 views

Central angle of a circular sector from area and arc length

I've been doing a task which says the following: Area of a circular sector is $3.2\pi cm^2$, arc length is $0.8\pi cm$. What is the central angle? I've been attacking this from several angles ...
1
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1answer
33 views

Circle passing through intersection points of two bigger circles

Suppose the equations of two intersecting circles are given.Now how to find the equation of circle passing through the points of intersection of the larger circles? Now please dont tell me that i got ...
0
votes
1answer
36 views

Circular motion of a particle with increasing speed.

I have researched angular acceleration and circular motion on google, but haven't found what I am looking for. I hope you can help me find more information about the problem below, with particular ...
1
vote
2answers
42 views

geometry question-semicircle inscribed in quadrilateral.

there is a line AD whose midpoint is O (AO=OD). a semicircle is drawn with centre O and any radius < AO with its straight edge being part of line AD. lines AB and CD are drawn tangent to the ...
4
votes
0answers
59 views

Writing circles as $|z-a| = \lambda |z-b|$ for the same $a,b$

My problem is in the context of the complex plane. I want to know if given two disjoint, not concentric circles $C_1,C_2\subset \mathbb{C}$, can you find $a,b\in \mathbb{C}$ such that $$C_1=\{z\in ...
1
vote
1answer
57 views

BMO1 2009/10 Question 4 Geometry Problem

Two circles, of different radius, with centres at B and C, touch externally at A. A common tangent, not through A, touches the first circle at D and the second at E. The line through A which is ...
0
votes
1answer
19 views

converting a circle's equation not touching axis to polar from Cartesian system for integration

I am having a really hard time figuring out how to convert this circle to polar coordinates, I am to use double integration after converting it. I know that $\theta$ has to be between $0$ and $\frac ...
0
votes
0answers
17 views

Calculate the overall circle enclosing multiple smaller circles

I have multiple smaller circles of a fixed radius that I am using to define a larger enclosing circle. So I'll need to find the x and y and radius of this new circle. I am looking for efficient over ...
1
vote
1answer
24 views

kth root of an open set in the circle toplogical group

My intuition tells me that in the topological group of the circle, if I take an open set U, then its kth root (where k is some natural number) in the circle is also an open set. In order to show it I ...
0
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0answers
9 views

Cover a rectangular with circles with different radius

I have a question about covering a rectangular with a set of circles, which is similar to this problem. I have a rectangular, say 1 meter by 2 meters. The whole rectangular is segmented horizontally ...
0
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1answer
48 views

Gradient function of a circle

The parametric equations of a circle $C$ are: \begin{align*} x&=2+\dfrac{13}{5\sqrt{2}}\cos t\\ y&=1+\dfrac{13}{5\sqrt{2}}\sin t \end{align*} for $t\in[0,2\pi]$. I am stuck on this part: Find ...
0
votes
1answer
87 views

Writing 1+1= 2 in a complicated way

I am learning Unit Circle at the moment and I am using this source as an education tool Trigonometry: Unit Circle (Starts at 20:00). The author solves these simple equations like below: ...
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2answers
45 views

Length and breadth of a rectangle enclosed between two semi-circles of given radii

34. It is required to take a rectangular frame in a horizontal position along a corridor bounded by vertical walls of which a horizontal cross-section is two concentric semicircles of radii $r$ and ...
0
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0answers
68 views

Simple Math\Geometry Question about Circles, etc

I never took Geometry in school, and although I went all the way to stats in college, all the brain surgeries I had made it really hard for me to do the simplest math for some unknown reason. So I'm ...
2
votes
3answers
56 views

Different ways to prove that area of circle with radius $r$ is $A=r^2\pi$

I want to compute the area of a circle in different ways. I know that any circle with radius $r$ have area $A=2\int_{-r}^r\sqrt{r^2-x^2}dx=r^2\pi$, but I want to prove it in other ways. My first way ...
0
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1answer
23 views

flat approximation of a circle at a point

I need to find a flat approximation of a circle at a given point. The circle I am working with is $$x^2+y^2=\frac9 4$$ The point is $(1,\sqrt{\frac 5 4})$ I have found an approximation, but it is ...
2
votes
2answers
67 views

Maximum area of a rectangle

Two concentric circles have radii 13 and 15. Let ABCD be a rectangle, so that A and B lie on the larger circle, and C and D lie on the smaller circle. Find the maximum area of rectangle ABCD. I tried ...
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1answer
38 views

Tangent - point of contact [closed]

I want to find out the co-ordinate of point of contact of tangent to a circle from external point when its center and radius are known. Please Help
0
votes
1answer
25 views

21' round pool in a square.

How big of a square would I need to fit a 21'round pool in with an extra foot on all sides.I was 23' or 24'.I also thought the radius plus a foot. However it has been 6 years since my last college ...
5
votes
4answers
236 views

Locus of a midpoint

Let $Γ_1$ be a circle of radius $4$, and let $Γ_2$ be a circle of radius $14$. The distance between the centers of $Γ_1$ and $Γ_2$ is $25$. Let $A$ be a variable point on $Γ_1$, let $B$ be a variable ...