For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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455 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 ...
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1answer
77 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 ...
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1answer
187 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
882 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
1k 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 ...
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1answer
441 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.

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, ...
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2answers
52 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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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.
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1answer
69 views

Find the circle which passes through two points

Find the equation of a circle which passes through $(4,-3)$ and $(-3,-4)$ with radius $5$. I tried putting the $x$ and $y$ into the equation $(x-h)^2 + (y-k)^2 = r^2$, but then I don't know how ...
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3answers
94 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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1answer
358 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 ...
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1answer
118 views

determine shortest distance between circle intersections

I have three circles positioned shown in the fig. Each of them has the same radius. I know the distance between each of them (A-B, B-C, A-C). My goal is to find the shortest path between B and C. The ...
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1answer
386 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 ...
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1answer
120 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
57 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 ...
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1answer
213 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 $x=0$.
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1answer
55 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 $(ABC)$ ...
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1answer
135 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
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3answers
876 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).
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1answer
83 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 ...
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2answers
4k 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 ...
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2answers
104 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 ...
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2answers
308 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 ...
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4answers
591 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 ...
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4answers
90 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 $x$: $$ (x - c_x)^2 + (y - c_y)^2 = r^2 $$ with a tangent line that also goes through a point $p$ lying outside the circle. ...
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2answers
116 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 ...
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0answers
279 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
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1answer
49 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 ...
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1answer
94 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 ...
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3answers
65 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 ...
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3answers
91 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 $x$ ...
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1answer
152 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 ...
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2answers
505 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 = ...
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1answer
77 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 ...
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0answers
155 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 ...
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2answers
51 views

Tangent - point of contact

Question: Tangent to the curve $y = x^2 + 6$ at point P(1, 7) touches the circle $x^2 + y^2 + 16x + 12y + c = 0$ at a point Q. Then the coordinates of Q are: 1) $(-6, -11)$ 2) $(-9, -13)$ 3) $(-10, ...
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2answers
63 views

Circle - finding the equation

Question: A circle touches the lines $2x+3y+1=0$ at the point (1, -1) and is orthogonal to the circle which has the line segment having end points (0, -1) and (-2, 3) as the diameter. What is the ...
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3answers
152 views

Solve the length AB (the dashed line)

Can someone show me how I can solve this? (Step by step example with solution appreciated a lot as I am currently practicing). EDIT: After a closer look, it looks as if this is an Isosceles ...
2
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3answers
262 views

The “Circle” is a Vector Space?

Consider the set of angles $C = [0, \ 2\pi)$ and, for all $x,y \in C$, define the $sum$ operation as the sum modulo $[0, \ 2\pi)$. The identity element of the addition is the angle $0$. The inverse ...
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2answers
49 views

Radius of a curvature

I have a lens (magnifying glass) and I want to calculate the radius of the curvatures on its sides. The lens in question diameter of the lens = 6 cm thickness at center = 7 mm thickness at edge = ...
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1answer
174 views

length of secant line.

I'm looking for way to find the length of a secant line intersecting another line through the center of a circle with a known radius. The intersection point is on the circle and the angle between 2 ...
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2answers
54 views

Circles - tangent from common point

Given the equation of a circle and the points of contact of two tangents, is it possible to find their point of intersection? The obvious method is to find the equation of the two tangents, using the ...
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4answers
301 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 ...
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1answer
105 views

Inscribed Circles in Triangles

This question appeared in this year's UNSW Maths competition. It was question 5b and it was the only question that i couldn't do. Sorry if my explanation is bad as it is complicated to understand ...
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3answers
68 views

Finding the variable of a coordinate point on a circle

This might be a very simple question but I am having trouble figuring it out, so if anyone can explain: A circle is marked with three points A(-3,2),...
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2answers
3k views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
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2answers
2k views

Geometry problem involving infinite number of circles

What is the sum of the areas of the grey circles? I have not made any progress so far.
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2answers
52 views

Solving for $\theta$ in a circle

Let's say you have a pendulum hanging straight down and touching the ground at the lowest point. The pendulum has length $l$. If you pull the pendulum back so that the end is height $h$ above the ...
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1answer
45 views

Rules of Inscribed Angles

https://www.dropbox.com/s/chbs2vilr9wjkvz/20140819_130744.jpg Image of question found above. I don't understand why angle BCD is formed by tangent and chord and is equal to 1/2 of arc BC.
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2answers
153 views

Placing a circle in a square lattice

Two part question. Consider the square lattice $\mathbb{Z}^2$: Imagine you are going to place a circle of radius $r$ somewhere in $\mathbb{R}^2$. Question 1: What is the radius of the largest ...