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

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2
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1answer
44 views

One special case of Helly's theorem (for $\text{radius}=1$ circles)

There are $n$ points on the plane. Any $3$ of them can be covered with a radius $1$ circle. Prove that there is a radius $1$ circle that covers all the points. Came to this when tried to prove an easy ...
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0answers
20 views

Non intersecting chords. [duplicate]

This was a question in a math contest and it just blew me. We are given n points on circle, without any coordinates and radius. Our aim is to derive an expression in n for number of ways in which: ...
3
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2answers
20 views

Does the radius of the quadrant pass from the center of the inscribed circle?

In the following picture: The smaller circle is inscribed inside the quadrant, whose radius (OB) is 8. The original question (but not the question of this post) is that "find the radius of the ...
2
votes
1answer
36 views

Circle bisecting the circumference of another circle

If the circle $x^2+y^2+4x+22y+l=0$ bisects the circumference of the circle $x^2+y^2-2x+8y-m=0$,then $l+m$ is equal to (A)$\ 60$ (B)$\ 50$ (C)$\ 46$ (D)$\ 40$ I don't know the condition when one ...
0
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0answers
12 views

Find Intersection of Two Circle given Lat/Lon and radius

I am attempting to calculate the intersection of two circle on the Earth with a given latitude, longitude and radius. I started with this post. While I am using this in the context of programming, it ...
1
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3answers
54 views

How can I find the co-ordinate of where a line intersects a circle?

I was looking to know if there was an equation that would allow me to calculate the co-ordinates of a point on the circumference of a circle where a line intersects it and the center. My diagram ...
2
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5answers
73 views

Find the equation of the circle.

Find the equation of the circle whose radius is $5$ which touches the circle $x^2 + y^2 - 2x -4y - 20 = 0$ externally at the point $(5,5)$
0
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1answer
28 views

3 Points in 3D Space to Develop an Arc or Circle

Background: I'm a Robotics Engineer and I am trying to develop a more flexible, modular, and robust program for our welding robots, which will minimize teaching time for new robots and also minimize ...
1
vote
1answer
72 views

Are ther situations when 3 points do not lie on a circles?

Consider 3 points on a plane, points are real. Is it possible that the points are placed in a way that makes it impossible to draw a circle trough them. I know that if the point forms a line then ...
0
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1answer
11 views

Find point on circle's tangent based on point on circle, radius and angle

The circle is centered at (0,0)"P" with a radius of 5. I have a point on the circle at (4,-3)"A". How would I find the points "B1" and "B2" on the tangent through point "A" given an arbitrary angle ...
2
votes
3answers
60 views

Drawing circumference issue

I'm a developer, and I'm developing an app on Google Maps. At the moment, I'm trying to draw a circle on the map. For getting all the points I need, I'm using the following formula: \begin{equation} ...
0
votes
1answer
91 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 $[+\theta, -\theta]$ ...
0
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0answers
24 views

Determine clockwise or anticlockwise

I have a central point define by an x and y and I have an object which is moving around it with a location defined by an x and a y. I'm trying to determine if the object is moving clockwise or ...
0
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1answer
397 views

Calculus Riemann sums for circle and ellipse

I ran into this problem today. I need to compare the Riemann sums for a circle and an ellipse. I have no idea as where to start. Here's the question:
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0answers
88 views

Comparing The Rates at Which Squares and Circles Fill Large Similar Areas.

Consider these two search patterns. ${\square}$ A square moves in straight lines forming what you might call a "square-spiral" pattern as it covers a much larger square space. ${\bigcirc}$ A circle ...
0
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2answers
52 views

given 3 circles, find relation of the regions

I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard. I had no idea how to find it nor where to start Note ...
1
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2answers
60 views

What is the homeomorphism between a disk and an ellipse?

A disk/circle is defined by $$C = \{(x,y) \in \mathbb{R^2} : x^2 + y^2 \leq r^2\}$$ An ellipse is defined by $$E = \{(x,y) \in \mathbb{R^2}: x^2/a^2 + y^2/b^2 \leq 1 \}$$ How can we define a ...
6
votes
1answer
558 views

Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
0
votes
1answer
62 views

Calculating another point on a circle from radiants

I have a program that tells me the angle in radians of a cursor from another item, let's say it's a star. What I want is to take this $(X_2,Y_2)$ point and deviate it a bit on the left or right ...
1
vote
2answers
401 views

Bounding box enclosing circles, that complies with ratio constraints

Given a circle centered at $A$, with radius $R_a$ and another radius $R_b$, I need to find a center for circle $B$ such that both circles are tangential, and the bounding box including both circles ...
0
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3answers
28 views

Scalene triangle with semicircles mensuration

I was recently going through a mensuration sum from a tenth grade board exam book. This one particular question stumped me, and I spent the entire evening thinking of this, but to no avail. The ...
0
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1answer
14 views

Creating Polynomial Function with Surface Area of Cylinder

I've spent a few hours at this question but can't seem to get the right answer. I was hoping someone here can lead me in the right direction. The question: A storage tank is to be constructed ...
13
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8answers
31k views

How can I find the points at which two circles intersect?

Given the radius and $x,y$ coordinates of the center point of two circles how can I calculate their points of intersection if they have any?
2
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4answers
120 views

how to prove that the circle $(x-a)^2+(y-b)^2=a^2+b^2$ is passing through point $(0,0)$

How can one prove that the circle $(x-a)^2+(y-b)^2=a^2+b^2$ is passing through point $(0,0)$? I know that if i put: $x=y=0$, i will get: $(0-a)^2+(0-b)=a^2+b^2=a^2+b^2$ But that's not a proof but ...
1
vote
1answer
33 views

Angle of intersection of the given curves.

What is the angle of intersection of $$[|\sin x| + |\cos x|]$$ And the curve $$ x^2 + y^2 = 5 $$ where $[n]$ denotes greatest integer function. This is a homework question. I have tried to find the ...
0
votes
1answer
67 views

Two circles defining a line

We have two dots $d_1,d_2$ moving on circles $C_1, C_2$ with radii $r_1, r_2$. The circles are moving at speed of $s_1, s_2$. A line is drawn between $d_1$ and $d_2$. When does this line have some ...
1
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1answer
341 views

Inner tangent between two circles formula

As a programmer I need to draw the inner tangents between two circles, but only the segments, not the whole line. But the internet is surprisingly hostile to lazy programmers who don't know their ...
3
votes
5answers
6k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
3
votes
4answers
30k views

How to find the equation of a line tangent a circle and a given point outside of the circle

I am given the equation of a circle: $(x + 2)^2 + (y + 7)^2 = 25$. The radius is $5$. Center of the circle: $(-2, -7)$. Two lines tangent to this circle pass through point $(4, -3)$, which is outside ...
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2answers
255 views

How many coordinates are necessary to determine a sphere?

Do determine a circle, you would need at least three coordinates. How many are necessary to determine a sphere?
3
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4answers
379 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 $(x_0, y_0, z_0)$?
2
votes
6answers
14k views

How to prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact?

I've tried drawing a parallel chord to the tangent but then how would you prove that the chord is perpendicular to the radius?
3
votes
2answers
63 views

I got stucked in middle of the problem. How to find the value of radius 'x' cm from the given figure?

![enter image description here][2] Firstly, I calculated the area of sector $AOB$ by applying $\frac{1}{2}\times (1.2\ \text{radians})\times 20^{2}$ (formula for area of sector of circle) and ...
1
vote
4answers
348 views

How to find the intersection point of two moving circles?

I'm trying to develop a simulation in C#, and I have to find the intersection (or collision) point of two moving circles, in 2D space. Actually one of my circles will be stationary, so only one of ...
1
vote
4answers
121 views

Circles - point of intersection of tangents

Question: Let A be the center of the cricle $x^2 + y^2 - 2x-4y-20=0$. Suppose that the tangents at the points B(1,7) and D(4,-2) on the cricle meet at point C. Find the area of the quadrilateral ABCD. ...
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0answers
36 views

An equivalent definition of the rotation number of a circle homeomorphism

Let $f : \mathbb S^1 \to \mathbb S^1$ be an orientation-preserving homeomorphism. The classical definition of the rotation number is the following: we lift $f$ to a homeomorphism $F : \mathbb R \to ...
0
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1answer
185 views

max points in circle given radius and min spacing between points

I want to know how many points ($n$) can be placed in a circle of radius $r$, with a minimum spacing $s$ between points. I find postings for several similar problems -- smallest circle around a set of ...
0
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2answers
146 views

Is that possible that a inscribe angle can be greater than 90 degree

I have found a question like following: Its asked that what could be the angle $x$ if $BC$ is not diameter of the circle. So, my question is if it possible to be greater then $90^{\circ}$ for an ...
-1
votes
5answers
54 views

distance between centres of two overlapping congruent circles

If there are two overlapping congruent circles such that the area of intersection is 10% of the area of each circle, what is the distance between their centres in terms of the radius r cm?
0
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2answers
32 views

Find a bisector point of a circle

The coordinates of $A=(x_{0},y_{0}$) and $B=(x_{1},y_{1}$) are given. How to find the coordinates of $C$ and $D$ as per given information below. ABC is equilateral triangle such that $AB=BC=CA$ ...
1
vote
1answer
35 views

Equation for spacing of elements on the edge of a circle

I'm trying to come up with an equation which, given an index within an arbitary number of elements (the most natural example would be 12, as in 12 numbers on a clock), along with an arbitrary radius, ...
0
votes
1answer
39 views

What is the area of the shape defined by the locus of a point on a circle rolling around another circle?

What is the area of a shape, which I'm deeming a 'cylicoid', which is defined as follows: Circle A of radius 1 is held stationary. Circle B of radius 1 has a point on its rim which traces a path as it ...
3
votes
1answer
140 views

Find Area of 3 Sector Circle, Variable center point

I have a Circle separated into 3 sectors. At start each sector has the same central angle, 120°. Therefore each sector should be taking up the same area. I want to be able to move the center point ...
1
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1answer
346 views

Finding the points of a circle by using one set of coordinates and an angle

I know the image below isn't to scale and that the angle isn't quite at the centre point but can we just imagine it is picture perfect.... I know the coordiantes and point (x,y) lets say they are ...
0
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2answers
44 views

Help me find the point of intersection of a line and a point. [duplicate]

Find the equation of the circle with its center at $(-1,-3)$ and tangent to the line through the point $(-2,4)$ and $(2,1)$. The line is $3x+4y=10$ and the point is $(-1,-3)$. What's the better ...
0
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0answers
25 views

Area of equilateral triangle from circumcircle

I am trying to calculate skewness of triangle. Given the sides of a triangle (not equilateral), I calculated circumradius from which I would like to get area of equilateral triangle.
0
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2answers
893 views

Angle between tangents and angle subtended by radii are supplementary

Using the result that the length of the tangents draw from an external point to a circle are equal, prove that the angle between the two tangents drawn from an external point to a circle is ...
0
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2answers
347 views

Circle touching the $y$-axis passing through two points

How to find the equation of the circle touching the $y$-axis given that it passes through two particular points?
0
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1answer
55 views

Condition for this set of points

This is for a calculator experimental prob. simulation. So, there is circle in a square and the circle is touching all 4 sides of the square. We need to first choose a coordinate system (two ...
0
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1answer
303 views

Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...