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

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1answer
14 views

Length of tangent line segment to 2 circles

https://drive.google.com/file/d/0B-4lJHUDH1P5UEZ4QzNYcTNYQWs/edit?usp=sharing The image of the problem can be accessed in the above website. Two semicircles are tangent to each other. The ...
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0answers
24 views

Count balls to put in triangle

Given balls of radius $R$ we need to find how many balls can be put into a triangular container with sides $a,b$ and $c$. Example : Let $R=1$ and $a=3,b=4$ and $c=5$ then answer is $1$, as only one ...
1
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1answer
32 views

Area of shape made from quarter arcs of circles

I have this task. I would first calculate the square that I marked red. That's $6\times 6=36$. Then I add one circle with area $(1.5)^2\times \pi$. So the answer is E, because the area is $36 + 2.25 ...
3
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1answer
28 views

How to maximize area of two circles inside a rectangle without overlapping?

Two circles have to be drawn inside a rectangle of dimensions $W\times H$ such that the area of both circles is to be as large as possible without overlapping. Let the radii of the circles be $r_1$ ...
0
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1answer
21 views

equation for the radius of a circle that is tangent to two lines and passing through a specific point on one of the lines?

I'm interested in finding the equation for the radius (and optionally the center point) for a circle that is tangent to two lines and passing through a specific point on one of the lines. So far, I've ...
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0answers
19 views

Position n circles in circular layout

Given an index from 1 ... n, and a fixed width and height of each circle (and a fixed spacing), how would I calculate the center x coordinate and center y coordinate of each node to match the ...
2
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0answers
60 views

Prove that $3$ points are collinear

$\triangle ABC$ is any triangle, $BD$ is its angle bisector. Everything else on the diagram is as you see it, except we are not sure if $I,K,D$ are collinear. How to prove it? Of course, $E$ is not ...
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0answers
22 views

Significance of Orthocenter in real life

I have found that the circumcenter, incenter, and centroid have some connection with real life, for example centroid is used to find the center of mass of a 2d object.. however I am unable to find the ...
2
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1answer
29 views

Find the equation of line and finding a point in given example

The outer circle is $x^2+y^2=1$ and the smaller circle is $x^2+(y+1-r)^2=r^2$. The arclength is parameterised anticlockwise with $s=0$ at the bottom as shown. If we know $s_n$ and $s_{n+1}$ can we ...
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0answers
11 views

distance between random points in two non-overlapping circles [duplicate]

I have had asked a question yesterday, got a link of the book but can not find it anywhere to buy or loan. Can any one point me towards a formula or distance distribution for distance between two ...
0
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1answer
33 views

Number of integer lattice points within a circle

I am trying to solve a problem on codeforces, to be precised, this problem. I was able to figure out that the solution is $N(n) - N(n-1)$ where $N(n)$ is the number of lattice points withing a circle ...
2
votes
1answer
34 views

Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to ...
1
vote
1answer
59 views

Can $\pi$ and the $\pi$ in radians simplify?

I saw in a proof for the limit $$\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1$$ that, in one of the steps, you had to take the area of a section of a circle, in which you had to do $\frac{\pi r^2 ...
3
votes
1answer
29 views

Longest chord inside the intersection area of three circles

I am currently working on my masters thesis in computer science and I stumbled onto a geometry problem. My goal is to compute the length of the longest possible chord inside the intersection area of ...
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1answer
29 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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1answer
22 views

Geometry Find the Radius of a circumcircle given the area of the triangle

Ok so here is what I know, the circumcircle of an equilateral triangle with an area of $4\sqrt{3}$ is drawn, calculate the radius lenght of the circumcircle. I also know that to find the radius I ...
1
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1answer
35 views

If$ x^2 + y^2 + Ax + By + C = 0 .$ Find the condition on $A, B$ and $C$ such that this represents the equation of a circle.

Also find the center and radius of the circle Here's my solution, I'm not sure if it's correct or not (specifically the conditions on $A$, $B$ and $C$. I feel that my conditioning is invalid and that ...
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2answers
38 views

Circle equations

Given that the circle C has center $(a,b)$ where $a$ and $b$ are positive constants and that C touches the $x$-axis and that the line $y=x$ is a tangent to C show that $a = (1 + \sqrt{2})b$
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2answers
37 views

equation of circle tangent to line with radius

Find the equation of a circle tangent to line $3x + y - 2 = 0$ at $(-1,5)$ and with radius $\sqrt{10}$. I've no idea on how to do this.
1
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1answer
36 views

Circle pass through 2 ponts with radius

Find the equation of a circle pass through (4,-3) and (-3,-4) with radius 5! I tried putting the x and y to equation(x-h)^2 + (y-k)^2 = r^2 then I don't know how to continue
2
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3answers
49 views

In what sense is a function on a circle the same as a $2 \pi$ periodic function on $\mathbb{R}$?

I was reading the appendix of Elias M Stein's Fourier Analysis and before proving the approximation lemma the author mentions the following Recall that a function on a circle is the same as a $2 ...
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2answers
84 views

How to find the equation of a circle given 2 points [closed]

The Circle C touches the y-axis at the point A (0,3) and passes through the point B (2,7). Find the equation of C
1
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1answer
27 views

General solution for intersection of line and circle

If the equation for a circle is $|c-x|^2 = r^2$ and the equation for the line is $n \cdot x=d $, and assuming that the circle and line intersect in two points, how can I find these points? Also as ...
0
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1answer
16 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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0answers
24 views

Estimating the mean internal distance between borders of an irregular shape

I have two overlapping (not matching) irregular shapes ($X$ and $Y$), and I would like to estimate the mean distance between their limits. What I've been trying so far is obtaining the irregular ...
0
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1answer
9 views

A,B,P are three points on a circle having centre O. If angle OAP=25 and angle OBP=35 , then the measure of angle AOB is???

A,B,P are three points on a circle having centre O. If angle OAP=25 and angle OBP=35 , then the measure of angle AOB is???
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3answers
26 views

Calculate the circumference of a circular lake

A lake has a diameter of $7$m and needs to be fenced for the protection for children. What length of fencing is required? Fencing comes in $1$m lengths, how many lengths are needed? What is the ...
1
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1answer
68 views

Finding equation of tangent of a circle that intersects the origin?

Given: circle with equation $(x-2)^2+(y-1)^2=4$. How to find equation of tangent line to the circle that intersects the origin? I easily found out that one of the tangents is $x=0$.
1
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1answer
47 views

Prove that the triangle areas are proportional to the radii

The line $MN$ is the radical axis I created. Because of its properties, we have $EM=MF, HN=NG, IQ=QL$, and it is perpendicular to $AC$. Everything is as you see on the diagram below. Here $(ABC)$ ...
3
votes
0answers
57 views

What is the 'optimal' equal-area partition of a circle?

What is the (an?) n-partition of a circle that meets the following criteria: The boundaries of each partition can be represented as a union of finitely many finite-piecewise-smooth simple closed ...
2
votes
3answers
61 views

Diameter of a circle touching three inner circles of diameter 1

If the diameters of three three inner circle are $1$ meter, what is the radius of the big circle? (Note: the OP provided own answer below, after getting a hint).
0
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1answer
30 views

Algebraic proof for sphere/circle overlap formula

Two spheres or circles denoted by center position vector and radius $ p_0, r_0$ and $p1, r_1$ will overlap if $$ |p_0-p_1| < r_0+r_1$$ I understand geometrically why it works, but how would one ...
1
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2answers
39 views

Finding the exact area of a circle?

Background: I recently began taking calculus and it has come to alter the way I look at circles, and curves. The equation of a circle is $\pi r^2$, traditionally in school we have always left the ...
0
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2answers
21 views

Co Ordinate Geometry Of The Circle

Hi hello this is my last resort as I have no clue how to do these sort of sums and need help badly. Find the equation of the tangent to the given circle at the given point Circle (x - 4)² + (y + 2)² ...
0
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1answer
40 views

AB is the chord of circle with centre O and DOC is a line segment originating from point

AB is the chord of circle with centre O and DOC is a line segment originating from point D on the circle and intersecting AB produced at C such that BC=OD.IF $\angle BCD=20degree$ then$\angle AOD$?
2
votes
2answers
61 views

How can I visually imagine the area of a circle divided by $\pi$?

If I have a circle with an area of 100 units^2, and I divide it by $\pi$, how can I imagine that visually in my mind? Since 100 / $\pi$ =~ 31.83, and the square of that is =~ 5.64, I currently ...
0
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2answers
36 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 for an angle like x? ...
1
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4answers
106 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 ...
0
votes
4answers
73 views

Given circle and point, where does the tangential line through the point touch the circle?

Given a circle with known center $c$, known radius $r$ and perimeter point $p$: $$ (x - c_x)^2 + (y - c_y)^2 = r^2 $$ with a tangent line that also goes through a point $pp$ lying outside the circle. ...
2
votes
2answers
65 views

Any two points inside a circle are within a diameter of each other.

In many problems involving the Pigeonhole Principle, we often assume the following lemma: Lemma: The distance between any two points in a circle of radius $r$ is at most $2r$. Intuitively, this ...
1
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0answers
23 views

Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...
2
votes
1answer
31 views

Equation of circle - from chord

Question: If one of the diameters of the circle $x^2 + y^2-2x-6y+6 = 0$ is a chord to the circle with center (2, 1), then the radius of the circle is: $\sqrt3,\sqrt2,3,2$ I have no clue as to where ...
0
votes
1answer
49 views

Circles and tangents and circumcircles

Question: Tangents drawn from the point $P(1, 8)$ to the circle $x^2 + y^2 -6x -4y -11=0$ touch the circle at the points $A$ and $B$. What is the equation of the circumcircle of the triangle $PAB$? I ...
1
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3answers
33 views

Compute the set of points (x,y) for a circle of arbitrary radius, with a 1 degree step, without using any trigonometric function.

Is it possible for a computer program to geometrically construct a approximate circle (pixels have line drawing limitations) without using any trigonometric function? e.g. taking the unit circle as ...
2
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3answers
48 views

How to find the radius of this middle circle arranged as shown.

There is this maths competition geometry problem and my approach. And this is my initial approach. From the picture, the shaded circle looks slightly bigger. What we are looking for is the $x$ ...
1
vote
1answer
31 views

Homeomorphism of a Genus-2 Surface

Does there exist a homeomorphism from a genus-2 surface, the connected sum of 2 tori, to two circles, $S^1$, intersecting at a point? Intuitively it seems that the double torus can be squeezed into ...
3
votes
2answers
47 views

Midpoint of chord of contact

Question: The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4x - 5y = 20$ to the circle $x^2 + y^2 = 9$ is: a) $20(x^2 - y^2)- 36x + 45y = ...
-1
votes
1answer
59 views

How is circle closed?

I have this thought that circle in 'real' is not a closed figure. We all know that 'pi' is irrational.And integers are nodes in a 'monstrous' line of real numbers. Irrational numbers are ...
2
votes
0answers
40 views

Find circles that completely cover a polygon minimizing the amount of space covered outside the polygon

I have an arbitrary polygon that I need to roughly represent using circles. Any point inside the polygon must lie inside a circle. There will be points outside the polygon that will fall under a ...
0
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2answers
25 views

The length of the side of the square is 4 Find the radius of the smaller circle? [closed]

The length of the side of the square is 4. Find the radius of the smaller circle?