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

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6
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1answer
1k views

The number of circles that will fit inside the area of larger circle?

Let's say circle $\omega_1$ has a diameter $X$. Let $X>Y$; $Y\in \mathbf{R}^{+}$. How many circles with diameter $Y$ will fit inside $\omega_1$? Is there a formula for this?
24
votes
4answers
1k views

Finding an invisible circle by drawing another line

A friend of mine taught me the following question. He said he found it in a book a few years ago. Though I've tried to solve it, I'm facing difficulty. Question: You know on a plane there is an ...
2
votes
5answers
2k views

Finding the length of chord of a circle.

I'm trying to solve the following problem: The figure below shows that a circle of radius $r = 1$ is inscribed in quarter circular region $OPQ$. Find the length of the chord $AB$. I thought about it ...
7
votes
4answers
315 views

Why is $\pi r^2$ the surface of a circle

Why is $\pi r^2$ the surface of a circle? I have learned this formula ages ago and I'm just using it like most people do, but I don't think I truly understand how circles work until I understand why ...
7
votes
1answer
781 views

How to draw ellipse and circle tangent to each other?

The circle $c$ is given as are the points $A$ and $B$, which are ellipse's foci. Now I need to construct the ellipse that is tangent to the circle $c$ such that the points $A$ and $B$ are its foci. ...
0
votes
2answers
49 views

Get X and Y from circle angle

I want to extract x and y based on an angle. See below. So if the angle is 45 degrees, x would be 0.5 and y would be 0.5. The only way I can think of solving this would be to separate the circle ...
1
vote
1answer
160 views

Intersection point of 2 circles

I don't understand why equating the equations of two circles doesn't give their intersection point. Instead, it seems to give the line passing through the intersection points, and you have to again ...
3
votes
1answer
483 views

Minimize the sum of distances between two point and a circle

Let's $A$,$B$ and $O$ be random point in a plane, such that they are not colinear. Let's $c$ be a circle centered on $O$, such that points $A$ and $B$ are outside of it. Find a point $X$ that lies on ...
1
vote
1answer
453 views

Circle formula given two points and a manipulable radius

I need to find the formula for a specific circle. I know two points that is on the circle: (1,2) and (10,16) I need to be able to manipulate the radius, so that I can find the formula that I am ...
1
vote
3answers
319 views

Geometry problem on circles from a competition

Triangle $\triangle ABC$ is an equilateral triangle whose side is $16$. A circle meets the sides of the triangle at $6$ points: it intersects $AC$ at $G$ and $F$ and $|AG|=2$, $|GF|=13$, $|FC|=1$. ...
1
vote
2answers
208 views

Scaling points in circle

I have a set of points that fall inside of a circle with a radius of 1 and a center of 0,0. I want to know how to scale those points so that they all have a radius between .5 and .75. For example, if ...
3
votes
2answers
263 views

Calculating position/distance of point on arc of circle

I'm having a hard time trying to wrap my head around this problem. Imagine a line of length $A+B$ with center $C$, with a circle with $d = A+B$ with center at $C$. Now imagine drawing a line at ...
1
vote
2answers
226 views

A question on circle

I was solving sample maths paper and came through this question:- If a ball is dropped on ice having a diameter of 24cm and fill inside with depth of 8cm,find the radius of the circle drawn over ice ...
0
votes
2answers
1k views

formula for finding perimeter of half circle

i was looking for this problem http://www.majortests.com/gre/problem_solving_expl.php?exp=50313039243130243330 and was surprised if it is correct,we know that circumference or perimeter of circle ...
1
vote
1answer
321 views

Euclidean Circle Geometry Problem

Let $\Gamma_1$ and $\Gamma_2$ be two non overlapping circles with centers $O_1$ and $O_2$ respectively. From $O_1$, draw the two tangents to $\Gamma_2$ and let them intersect $\Gamma_1$ at points $A$ ...
5
votes
2answers
312 views

Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
0
votes
1answer
155 views

angle of inscribed triangle

let us consider following problem: we have inscribed triangle,like this we are asked to determine if given $x$ is acute or obtuse,$O$ is center of circle,as i know if $CB$ would be ...
3
votes
1answer
131 views

what does mean swept in lines?

suppose that we have following picture question is which of the following chords are parallel,suppose that all lines are chords and we are checking which of them is parallel 1.$a$ and $f$ ...
4
votes
2answers
589 views

Prove that the centre of the nine-point circle lies on the midpoint of the Euler line

In $\Delta ABC$, $AD, BE, CF$ are the altitudes and $\Delta A'B'C'$ is the medial triangle. $K, L, M$ are the midpoints of $AH, CH, BH$. Consider the nine-point circle with centre $G$ (not to be ...
0
votes
1answer
130 views

Möbius map of two circles to half planes

I am very new to complex analysis and am having some trouble with finding a Möbius map that will take two unit discs to half-planes. I don't have enough reputation to post images, but here is a link ...
0
votes
1answer
857 views

How to calculate the height of a circular segment based on the area.

Given an area of a circular segment, how can one find the height of the circular segment? In the image below, assume the area of the green segment is known. How can one find the value of ...
0
votes
2answers
150 views

A simple circle problem

There is a big circle of radius 20cm and a smaller circle 100 cm away from it of radius 5cm now imagine these two to be 2 tires connected by a chain , where the bigger one completes one rotation how ...
-1
votes
1answer
265 views

Concentric circles of radii 1, 2, 3, …upto 100 are drawn.

Concentric circles radii $1, 2, 3, \ldots , 100$ are drawn. The interior of the smallest circle is colored red and the annular regions are colored alternately green and red, so that no two adjacent ...
0
votes
1answer
4k views

relationship between circumference and revolution

i would like to clarify two things by this problem:first what is relationship between circumference and revolution and also revolution and distant traveled by round object.let us consider following ...
3
votes
4answers
4k views

Is it possible to build a circle with quadratic Bézier curves?

i'm searching for a curve type with a minimum of functionality and maximum of usability. I run into quadratic Bézier curves and i wonder, if its possible to draw a circle with it.
5
votes
1answer
602 views

Can anyone explain intuitively why increasing the circumference by 1 meter always increases the radius by 15.9cm?

I found the mathematical proof, and it is obviously correct. But how can the increase in radius be constant regardless of the starting circumference? With a very small circle, the increase should be ...
3
votes
1answer
120 views

Perimeter of a rectangle with four circles in each corner

my teacher asked a question in exercise for calculate the perimeter of following: I get result of $144\pi$ and some of my friends got $208.2$ as result (assuming $\pi\approx3.14$). Q: what's the ...
0
votes
1answer
113 views

Quadrangle with maximum area in circle

My question is related to my previous one find parameter for maximize area suppose we have $4$ points,with coordinate $A(2\cos t,2\sin t)$ $B(-\cos(2-t), -\sin(2-t))$ $C(-2\cos(t) ,-2\sin(t) )$ ...
0
votes
2answers
176 views

determine position of circle inside square

i need to determine position of circle inside square,let us suppose that we have following picture we have following informations: 1.$ABCD$ is square 2.all small figures ,$KMCE$,$PKEF$,$NPFD$ ...
1
vote
2answers
125 views

Fitting circle into an angle

I've been struggling with this for quite some time now, anyone could help me perhaps with this? Given an angle of an arbitrary degrees, and a circle with radius r. And imagine I would try to push the ...
3
votes
4answers
286 views

Finding the area, general case with angle $\theta$.

Inspired by this question, I am curious to know the more general case. Given the radius of the large circle as $R$ and the angle $\theta \le \pi$, what is the area of the colored section? My ...
2
votes
2answers
437 views

Proof: Invariant angle measure - same result for any circle drawn.

Below I have quoted Wikipedia. I am particular interested in the statement: The value of $\theta$ thus defined is independent of the size of the circle: if the length of the radius is changed ...
7
votes
3answers
382 views

find area of dark part

let us consider following picture we have following informations.we have circular sector,central angle is $90$,and in this sector there is inscribed small circle ,which touches arcs of sectors ...
5
votes
3answers
2k views

Proving the length of a circle's arc is proportional to the size of the angle

How can I prove that: The length of the arc is proportional to the size of the angle. Every book use this fact in explaining radians and the fundamental arc length equation $s = r\theta$. ...
1
vote
1answer
131 views

find area of square part

let us consider following picture where $ABCD$ is square, and using $A$ and $C$ as center,there is drawn arc,we should find area of dark part.we know that length of square is $a$,as i see the ...
0
votes
1answer
162 views

find minimum length of triangle

suppose that we have $ABC$ triangle,with $AB=28$ and $C=120$,we should find minimum length of triangle,if it is know that $AC:BC=3:5$,it is clear that minimum side is $AC$,also because sides are ...
1
vote
2answers
100 views

find angle in triangle

Let us consider problem number 21 in the following link http://www.naec.ge/images/doc/EXAMS/math_2013_ver_1_web.pdf It is from georgian national exam, it is written (ამოცანა 21), where word ...
4
votes
2answers
173 views

A proof in circles.

I need help proving this problem: $AB$ is a diameter of a circle. $CD$ is a chord parallel to $AB$ and $2CD = AB$. The tangent at B meets the line $AC$ produced at $E$. Prove that $ AE = 2AB $. ...
12
votes
4answers
2k views

Is it possible to divide a circle into $7$ equal “pizza slices” (using geometrical methods)?

Or is it possible to divide a circle into n equal "pizza slices" (I don't know how to call these parts, but I think you'll know what I mean), where n hasn't got a common divider with $360$? Or are the ...
1
vote
1answer
224 views

How to prove that a circle passing through the center of the circle of inversion invert to a line?

link to the referenced picture: http://www.flickr.com/photos/90803347@N03/9220374271/ In order to prove the Arbelos Theorem, as in the picture above, one need to prove that the semicircle $C$ invert ...
1
vote
2answers
395 views

Maximum Distance between points on circle

What is the greatest possible distance between two points: one on a circle with radius 1 and centre (1; 2) and the other on a circle with radius 2 and centre (4; 6) I am not familiar with the ...
1
vote
2answers
74 views

Points on a circle

36 points are marked, equally spaced, on the circumference of a circle. Some of the points are marked with crosses in such a way that the distances between every two consecutive crosses are all di ...
0
votes
0answers
137 views

Compute multiple Rectangles area intersect by a circle

I've a need to compute the area of single elements (dice) of a matrix like this: http://i.stack.imgur.com/EKVSz.jpg The matrix is composed by 'c' columns and 'r' rows and every element/rectangle has ...
3
votes
1answer
1k views

Determining the angle degree of an arc in ellipse?

Is it possible to determine the angle in degree of an arc in ellipse by knowing the arc length, ellipse semi-major and semi-minor axis ? If I have an arc length at the first quarter of an ellipse and ...
0
votes
2answers
54 views

Finding a point on a circle

I have a circle that I am trying to find series of points on. I know the radius and horizontal tangent point at the top of the circle. I need to find a point that lies on the circle's circumference ...
1
vote
1answer
52 views

Sectors of a Circle

I am programatically drawing sectors of a circle with radius 55 on a cartesian plane which runs from -55 to 55 on the x and y axes. I would like the first sector to be drawn at 0,55. I know I can ...
0
votes
1answer
83 views

Calculate x,y line terminiating point of section of a circle

I have a Cartesian plane running from -41 to 41 on the x and y axes and a circle centered on 0,0 with a radius of 41 divided up into a number of sections of different areas. I know the percentage ...
4
votes
2answers
327 views

Applonius Circle/ Ford Circle / Infinite GP / Circle Packing

All the smaller circles are mutually tangent and continue to infinity. What is sum of radii of all the smaller circles?
6
votes
3answers
14k views

How to determine the arc length of ellipse?

I want to determine the arc length of a ellipse. So what data should I know ? And what law should I use ? For example I have this ellipse on picture below: How can I determine the $d$ length of ...
1
vote
0answers
90 views

Circle in a simplex

Let $T$ be a $2$-dimensional simplex in $\mathbb{R}^2$. A circle $C(x,y,r) \subset \mathbb{R}^2$ is given by its center $(x,y) \in \mathbb{R}^2$ and radius $r\ge 0$. Show that the set of circles in ...