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

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24 views

Formula for a line segment (pair of end points) between two circles, minus the two radii. Simple?

I'm trying to construct a line segment between two circles. Given each radius and x,y center of each circle how can I find the endpoints for the blue line segment.
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0answers
21 views

Work back from atan2 please?

I have input from 2 axis which range from -1.0 to 1.0 and I convert that into degrees using the below formula. degrees = Math.toDegrees(atan2(axis1, axis2)) so an input of 1.0 and 1.0 gives a ...
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0answers
16 views

What radius circle to remove from unit circle to make golden earring? [on hold]

A circular lamina of radius $x$ is removed from a circular lamina of radius $1$. If the center of gravity is at the edge of the smaller circle (along the line connecting the two centers) what is $x$? ...
-1
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0answers
16 views

Coordinate Geometry Help (circles + trigonometry)

Question : Find all points $(x, y)$ {if there are too many then number of points is enough} which lie on or inside the circle $x^2 + y ^2 = 9$ and satisfying the equation $\tan^4 (x) + \cot^4 (x) + 2 ...
2
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1answer
31 views

“Reverse engineering” of a geometric illustration

The following enigmatic illustration can be found here, unfortunately without any accompanied comment or short description: Can you deduce its meaning? What was the way it was constructed?
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1answer
25 views

Question in finding final position in circle

im having difficulty solving this problem right now, I tried couple of times but i couldnt figure it out, can you please help and explain? thank you
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1answer
25 views

Integration: Find length of curve using NINT

Here are the questions - For question 4, part (b) gives a unit circle. But I'm unable to proceed with parts (a) and (c), since the curve is double valued for -0.5 Also, for question 6, integration ...
2
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2answers
55 views

Covering 1/8 of a circle

A circle of radius 1 is given, and 8 semicircles of radius 1/2, like in this picture: What is the radius of the smallest circle that can cover shaded area? There was another problem involving the ...
4
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3answers
45 views

Inverse of an ordered pair?

Let $f: A \to B$ be a bijective function where $A = [0, 2\pi)$ and $B$ is the unit circle. Find the inverse of $f(\theta) = (\cos\theta, \sin\theta)$. I don't understand what it means to take the ...
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5answers
58 views

Find third point to make isosceles triangle with a specific area

Using points A(1,2) and B(-2,-2), find a third point, with a positive y-value, that makes ABC an isosceles triangle with area 10 units${^2}$. I have found AB to be 5 and used this as $r^2$ below.. ...
6
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1answer
53 views

What is the equation to evenly distribute circles in a spiral?

What is the equation to evenly distribute circles in a spiral? I have attached a picture to show what I am trying to achieve and need to know what the equation is for this.
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0answers
20 views

How are 2D collision forces calculated?

Between 2 circles of the same radii, how can I calculate the collision forces to apply to each of the 2 circles? I have position, mass, and velocity for each of the circles. Here's what I have ...
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1answer
36 views

Calculating the length of a tangent drawn to a circle from a named point

My book (New Tertiary Mathematics Volume 1 Part 1, by C Plumpton and P S W Macilwaine) describes a method for calculating the length of a tangent to a circle from the point $(x_{1}, y_{1})$ outside ...
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0answers
21 views

Find the sub-area of a circle cut by chords [on hold]

Suppose a circle of area $A$ is given, and then cut off portions using chords of the circle. What is the resulting area based on such chords?
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0answers
31 views

Formula for area of circle made up of squares

I need to draw an approximate circle on a grid of squares and find its area. Each square must either be completely part of the circle or not at all occupied. Obviously, this means that it cannot be a ...
1
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0answers
39 views

2015 AMC12A question 25

This is a question from the 2015 AMC12 math competition. I haven't really made much progress at all on it, and I just want to know the right way to solve this equation. A collection of circles in ...
2
votes
1answer
43 views

Does this equation for a tangent to a circle have a name?

My Maths tutor showed me a shortcut way to find the equation of a tangent to a circle, given the radius, centre and point the tangent touches the circle: $$(x - a)(c - a) + (y - b)(d - b) = r^2$$ ...
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3answers
56 views

Find circle radius by given triangle inside

So the triangle inside the circle: $AB = 9$cm $CB = 6$cm $CH = 5$cm I think solving this problem involves similar triangles. Thanks in advance, I'd like to have a solution suitable for 9th ...
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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 ...
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2answers
31 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.
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1answer
49 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.
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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
98 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 ...
1
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0answers
27 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 ...
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3answers
49 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 ...
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0answers
36 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.
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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
52 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
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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
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0answers
27 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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1answer
76 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 ...
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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
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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 ...
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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
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2answers
32 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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0answers
25 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
26 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 ...
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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 ...
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votes
2answers
19 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 ...
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1answer
34 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
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2answers
26 views

Find a line parallel to a known line that intersects a known circle at one point.

There is a circle with an equation $x^2+y^2=16$ and a line with equation $y=x+1 $. The question is to find an equation of line placed parallel to this line and touching the circle at only one point. ...
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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
58 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
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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 ...