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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3
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0answers
164 views

Ellipses touching a circle

Given a circle and two points $A$, $B$ in the plane, how do I find an ellipse with focal points $A$ and $B$ that touches the circle? How many such ellipses are there (at least/at most)? Can I ...
1
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4answers
2k views

How do I move through an arc between two specific points?

I've found many answers to similar questions here, but I'm still stuck. I want to move an object from point sx,sy to point dx,dy through an arc that bulges by distance b from the line straight ...
1
vote
1answer
410 views

Circumcenter coordinates for a isosceles triangle

I'm back, wow, twice a day nowadays. I need to calculate circumcenter coordinates (or at least I hope they're called that) at point C for an isosceles triangle (the circle must be such, that created ...
11
votes
2answers
460 views

Is the figure the circumference of a unit circle?

A friend of mine taught me the following question. I've never heard such a strange and interesting question! Qustion: Supposing that a figure $S$, which is constituted by points, satisfies the ...
0
votes
1answer
76 views

Point of tangency for a circle between two vector

I'm having two vectors p and q starting at point O (origin). These vectors are known, as well as the origin point is. I know the angle α (alpha). Given a circle with arbitrary radius r, I want to be ...
0
votes
1answer
258 views

Chord passing through concentric circles.

A chord $AB$ of one of two concentric circles at intersect each other at $C$ and $D$. We have to prove, $AC=BD$. I am not sure what this question means by 'intersect each other', but if I am ...
2
votes
1answer
96 views

FFT on circular data?

You may have seen the demos of computing heart rate by looking at video, where they detect the face, compute a mean on the red channel from the face, submit the resulting mean-per-frame to an FFT ...
3
votes
0answers
90 views

Characterizations of a linear fractional transformation

Consider the function $$ g(t) = \frac{1+it}{1-it} = \frac{1-t^2}{1+t^2} + i \frac{2t}{1+t^2}. $$ (The second equality holds except when $t=i$.) It seems to be widely known that this function is the ...
0
votes
1answer
426 views

determine if pole is inside unit circle

i would like to know how to determine if pole of given function is inside unit circle contour? for example let us take this function $f(z)=(i-1)/(z+i)$ and we have contour ...
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2answers
89 views

How can I calculate the points of two lines that connect two circles?

Let's say I have two circles of equal or differing radii, a variable distance apart. I want to calculate the end points of two lines, that will "connect" the circles. And no matter how the ...
3
votes
0answers
59 views

Topology of a 3D wired Mandala?

There is a so called 3D-wired Mandala, based upon $2$ large circles each flowered symmetrically on its circumference by two sets of each $8$ half-circles. The circles are interconnected together by ...
-2
votes
1answer
94 views

“Aera” of square if “aera” of circle is passage in upper decimal

A circle with a radius of $5$ has an aera of $50$. What will be the aera of the square with a width of $10=2\times 5$? Do we need a ratio of diagonal/width to find this?
6
votes
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
343 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
858 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
51 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
171 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
520 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
512 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 ...
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vote
3answers
340 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 $|AG|=2$, $|GF|=13$, $|FC|=1$. ...
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vote
2answers
257 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 $0.5$ and $0.75$. ...
3
votes
2answers
326 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 ...
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vote
2answers
251 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 ...
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
366 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
314 views

Geometric Identities involving $π^2$

Are there any known geometric identities that have $π^2$ in the formula?
0
votes
1answer
170 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
153 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
655 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
137 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
1k 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
163 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
298 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
5k 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
661 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
130 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
120 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
195 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
134 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
297 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
472 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
395 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
190 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
114 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
174 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 $. ...