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

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1answer
780 views

internally and externally tangent circles

See the diagram here: diagram The diagram shows two circles of radius 1 and 2 tangent to each other and internally tangent to a circle of radius 3. What is the radius of the outlined circle ...
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163 views

Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum

I want the calculate the "value" of an angle in such a way that: The angle of 45 degrees corresponds with the maximum value of 1 The angles of 0 and 90 degrees correspond with the minimum value of 0 ...
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1answer
379 views

Meaning of this 4x4 determinant

Let $p,q,r$ and $s$ be four points on the plane. Moreover, $p,q,r$ are given in clockwise order. My book said that the following determinant is positive if and only if $s$ lies inside the circle ...
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1answer
193 views

Why do derivatives of certain equations relating to circles yield other similar equations? [duplicate]

Possible Duplicate: Why is the derivative of a circle's area its perimeter (and similarly for spheres)? We all know that the volume of a sphere is: $V = \frac{4}{3}\pi r^{3}$ and its ...
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2answers
227 views

Find the ratio in which the circle divides each of the sides AB and AC?

A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint . Find the ratio in which the circle divides each of the sides AB and AC? Does the line ...
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4answers
418 views

What is the radius of the circle in cm?

The rectangle at the corner measures 10 cm * 20 cm. The right bottom corner of the rectangle is also a point on the circumference of the circle. What is the ...
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3answers
1k views

Find the radius of the circle?

Two Circle of an equal of an radii are drawn , without any overlap , in a semicircle of radius 2 cm. If these are the largest possible circles that the semicircle can accomodate , then what is the ...
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1answer
2k views

Closest point on circle edge from point outside/inside the circle

Alright, I am programming a plugin for a game that requires me to get the closest point on a circle when all you have is a point B, which is outside of the circle, the radius of the circle, and the ...
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3answers
3k views

Find the length of the common chord

"Two circles with centres C1 and C2 and radius 6 cm and 8 cm respetively cut each other at right angles. Find the length of the ...
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1answer
3k views

Integer solutions (lattice points) to arbitrary circles

Wolfram Alpha will provide integer solutions to arbitrary circle equations. I'm trying to understand how it's able to calculate them, but despite a fair bit of digging I haven't found any discussion ...
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0answers
104 views

contradicting PI=4 fallacy. [duplicate]

Possible Duplicate: Is value of $\pi = 4$? I know that you can take area out of a square without changing it's perimeter. Now, here's this problem: Draw a circle with dia = 1; Draw a ...
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1answer
71 views

Computing angle

See the drawing for the situation. Given lenghts a, b and c and also L, but k and angle alpha are unknown. How to compute this angle alpha? I know it is possible to compute if we first compute k in ...
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2answers
438 views

Given an angle, get the trigonometric circle point.

Given an angle, in degrees, how can I get the trigonometric circle point coordinates for it? For instance, given the angle 0, I would get (1,0). 90 would be (0,-1). Clockwise.
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2answers
1k views

Calculate radius of variable circles surrounding big circle.

I got a circle, which I know all the details about him. (Radius [100], Diameter [200], Circumference [628.32], Area [31415.93]...) I would like to surround this circle, with smaller circles. I know ...
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1answer
905 views

Making a circle with paper folding, scissors, pencil, and a straightedge

Can we make a circle using paper folding, scissors, straightedge, anda pencil, allowing an infinite number of operations? I think my chemistry teacher have show me once how to make it during the ...
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1answer
136 views

Function for the upper left part of a circle

What is the function corresponding to the upper left quarter of a circle ? Where $x$ goes from 0 to $x_\text{max}$, and $y=f(x)$ goes from $y_\text{min}$ to $y_\text{max}$.
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1answer
132 views

Circle : How to get all co-ordinate list of circle parimeter?

I want to find all the co-ordinate of circle. I know the radius of circle and considering center co-ordinate as (0,0). So Is there any equation for finding all ...
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1answer
555 views

Tough Geometry Problem--Regular Polygon inside Circle

$ABCDEFG$ is a regular heptagon inscribed in a unit circle centered at $O$. $\ell$ is the line tangent to the circumcircle of $ABCDEFG$ at $A$, and $P$ is a point on $\ell$ such that triangle $AOP$ is ...
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0answers
566 views

Circle Packing Algorithm

I have question related to circle-packing. The problem is to find the circle of minimum radius enclosing four non-overlapping circles of arbitrary radius. I have to write a program in C for this ...
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1answer
709 views

How do you find the angle of circle segment formed with points (x,y) and (radius,0)?

I've been learning about the unit circle, sine, cosine, and the like in my introduction to trigonometry course, but I'm drawing a blank here. If I have a circle centered at the origin, with radius r ...
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1answer
2k views

Packing squares into a circle

I need determine the maximum number of squares of the given size that can be packed into a circle of the given radius. Squares can be rotated. I'm not sure how complex this problem is and i can find ...
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4answers
2k views

I need a proof that a line cannot intersect a circle at three distinct points

I need a simple proof that a line cannot intersect a circle at three distinct points.
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1answer
389 views

equation to get 10 points on circle surface at fix distance

What I tried is : $$x = \sin(36 \cdot 50 \cdot 3.14)/180$$ $$y = \cos(36 \cdot 50 \cdot 3.14)/180$$ Here $36$ is because I want 10 points on circle so $360/10=36$. $50$ is center X and center Y ...
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2answers
225 views

Area of a circle

I've tried to find as a personnal exercise where the formula $A=\pi R^2$ comes from. After drawing the problem, I've found that $A = 2\int\limits_{-R}^{R}\sqrt{R^2-t^2}dt$. How can I calculate this ? ...
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0answers
255 views

What “boundary conditions” can make a rectangle “look” like a circle?

I posted the question below in Stackoverflow but then realized that it perhaps would find a better audience here. I am solving a fourth order non-linear partial ...
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4answers
3k views

How to calculate the two tangent points to a circle with radius R from two lines given by three points

I need to calculate the two tangent points of a circle with the radius $r$ and two lines given by three points $Q(x_0,y_0)$, $P(x_1,y_1)$ and $R(x_2,y_2)$. Sketch would explain the problem more. I ...
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1answer
553 views

finding one circles radius so that it tangentially touches two other set circles

I am designing a water fountain on google sketchup and have run into a problem. I am designing the contours of the stone in the fountain. I would attach a picture of the problem but i need 10 ...
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2answers
429 views

Position of 3 circles intersecting at the centre of bounding box

Here's what I feel is a neat challenge: I'm building a data visualization comprised of 3 circles of dynamic sizes. I want to have them all intersect at the centre of a bounding box that will also be ...
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2answers
145 views

Trigonometry & circle math

I tried to solve this Trigonometry question, but I do not know how to solve. I read that the circle has radius 1 and center at (0.0) as the unit circle is plotted in the coordinate system. I ...
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1answer
2k views

how can I obtain enclosed area between two circles in cartesian coordinates?

In the diagram below (from here fig.2, page.5) the enclosed area between two circles (shaded area) has been indicated $a_{t+\delta_{t}}$. Can anyone help me how can I compute this? is it true? ...
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0answers
401 views

Pinwheel- perimeter of semicircular region

Above, we have a larger circle of $r=16$ with 8 equally spaced semicircles of radius=8. Each semicircle has one end on the larger circle's center and the other on the circumference of the larger ...
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4answers
317 views

Does the graph of $\cos x$ intersect the unit circle other than the point (0,1)?

It would seem the unit circle is nicely tucked under the graph of $\cos x$, touching only at (0,1), but is that what's truly going on here?
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1answer
172 views

Similar Right Triangles and Incircles [duplicate]

Possible Duplicate: Triangle and Incircle In a setup of right triangles ABC, BDA, and BDC not unlike this diagram (click on the link, and ignore the written side measures and subtext in ...
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4answers
614 views

Finding the equation of a circle

$A=(3,1)$ and $B=(-1,-1)$ are points on a circle of center $(k, -3k)$ find the value of $k$ I begin by assinging the values $\ g = -k $ and $\ f=3k $. I then substitute $(3, 1)$ and $ g= -k, f= ...
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1answer
98 views

Finding a point which is constrained to 3 other points.

Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points? Similar to this question, but with non-fixed minimum ...
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3answers
4k views

Circle and Line segment intersection

I have a line segment (begin $(x_1,y_1)$, end $(x_2,y_2)$, with $D=5$, let’s say) and a circle (radius $R$, center $(x_3,y_3)$) How can I check that if my line segment intersects my circle? picture ...
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2answers
223 views

Closest point to a unit circle from a point inside it

I'm working on a code at the moment that calculates the closest point to a circle from a point inside it. Let's say we have the point ($x_0, x_1$) to calculate the closest point to the unit circle it ...
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1answer
341 views

Determine larger arc from smaller arc

Given two angles (the starts and end of an arc), e.g. 90 degrees to 180 degrees, I need to output the starting and ending degrees of a small arc, and a large arc. In this case the small arc is simply ...
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2answers
506 views

Formula for the area of a segment of a circle… What am I doing wrong!?

Alright, I'm trying to study for a big test and I know that the area of a segment of a circle will be on it. Problem is, I can't seem to get the formula for it to work. I've gone over it countless ...
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1answer
211 views

Interval and Circle

Can anyone give me a proof of why the circle $S^1$ and the closed interval $[0,1]$ are not homotopically equivalent? (Using the basic definition and not the fundamental group!)
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1answer
132 views

Finding a function that computes a point on the unit-circle

I can't find the definition of a function $f(x); x \in [-1;1]$ where $(x|f(x))$ is a point on the unit-circle. Can you please give me a hint? ---------- Edit ----------- Background: I want to ...
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3answers
503 views

How to normalize this circle equation?

I am given a circle described by the equation below. Is there any way I can bring it to the form $(x-a)^2 + (y-b)^2 = c^2$ to have it be normal? My intent is to translate it to polar coordinates and I ...
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1answer
112 views

Circle locus, how to satisfy the equation.

$A(-3,1), B(0,-5), P(X,Y)$ If $|AP| = 2|BP|$ prove that $x$ and $y$ satisfy the equation: \begin{aligned} \ x^2+y^2-2x+14y+30 =0 \end{aligned} I get as far as determining the ...
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1answer
95 views

$D^n\times D^m\cong D^{n+m}$?

Let $D^n=\{x\in \mathbb{R}^n : ||x||\le 1\}$ the unit closed ball in dimension $n$, and $I=D^1=[0,1]$. We have $D^1\times D^1=I\times I\cong D^2$. Is it true that $$D^n\times D^m\cong D^{n+m}$$ ...
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3answers
988 views

Finding location of a point on 2D plane, given the distances to three other know points

I need to find location of the point $s_0$; the locations of other three points ($s_1$, $s_2$, $s_3$) are known. $d_i$ are known distances. Given: $x_1$, $x_2$, $x_3$, $y_1$, $y_2$, $y_3$, $d_1$, ...
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1answer
75 views

Unknowns in Circle Equation

The circle $x^2-y^2 + ax -2y -15 = 0$ contains the point $P(-6, 5)$. How would I find a?
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2answers
1k views

Area of shaded portion

Problem: To find area of shaded portion (AOB) in the below figure. Description of Figure: ABCD is a square of side 14 cm AOCD and BODC are quadrants
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3answers
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Is there a simple formula for this simple question about a circle?

What is the average distance of the points within a circle of radius $r$ from a point a distance $d$ from the centre of the circle (with $d>r$, though a general solution without this constraint ...
3
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2answers
5k views

Get the size of an area defined by 2 overlapping circles

I have two circles, like this: I know the radii of the circles, and I know the X + Y of the center of both circles. Can I get the size of the area that is black in my picture?
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5answers
2k views

finding center of circle

How can I calculate center of a circle $x,y$? I have 2 points on the circumference of the circle and the angle between them. The 2 points on the circle are $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$. The ...