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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1answer
59 views

Why is it wrong to naively pick random points inside a disk

According to MathWorld, the naive way to randomly pick points inside a disk, by using two uniformly distributed variables that are polar parameters: $r \sim [0, 1]$ and $\theta \sim [0, 2\pi]$, is ...
4
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1answer
61 views

Find radius of the circle analytically

Given the circle as seen in the attached image, find the radius of the circle analytically. Is that even possible? I know it can be found numerically. If analytical solution does not exist, can you ...
2
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1answer
38 views

Distance between incentre and centre of circle tangent to other sides

I was solving some geometry problems before I was stuck onto a problem. The problem says that if tangents from the $A$ point outside the circle are drawn, what would be the distance between the ...
7
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2answers
188 views

Finding an angle in a figure involving tangent circles

The circle $A$ touches the circle $B$ internally at $P$. The centre $O$ of $B$ is outside $A$. Let $XY$ be a diameter of $B$ which is also tangent to $A$. Assume $PY > PX$. Let $PY$ intersect $A$ ...
4
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2answers
86 views

Line tangent to circle

A circle with a radius of $2$ units has its center at $(0,0)$. A circle with a radius of $7$ units has its center at $(15,0)$. A line tangent to both circles intersects the $x$-axis at $(x,0)$. ...
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0answers
50 views

Basic Probability: choosing points at random on a circle

So, I know that the probability that three randomly choosen points on a circle will be on a semi-circle is 3/4 (as is discussed here: Probability the three points on a circle will be on the same ...
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0answers
27 views

Circle Packing of N Equal and Non Overlapping Circles in a Square

Given a square of side S in the Euclidean plane, what is the optimal packing of n equal and non overlapping circles within the given square? I have seen many conjectured theories of this problem, ...
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2answers
50 views

Find the length of PC [closed]

Here PE is the tangent of the two circle. PA = 12 ; CD/AB = 2 Find the length of PC [Source: BDMO] ]1
3
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2answers
62 views

Find the length of AB

In the diagram 4 circles of equal radius stand in a row in such a way that each circle touches the next one. $P$ is a point on the circumference of the first circle. The center of the fourth circle is ...
1
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2answers
61 views

Check if a point lies in a circle defined by three other points.

I'm learning Computational Geometry, and need to check whether a point p lies inside a circle defined by a triangle(made by 3 points $a,b,c$, in counterclockwise order). A very convenient method is ...
0
votes
1answer
56 views

How can one derive the circumference of a circle using integrals?

Many proofs for the area of a circle start with something like $$ A(r) = \int_0^r 2 \pi t dt $$ such as at https://en.wikipedia.org/wiki/Area_of_a_disk#Onion_proof , but I don't understand how to ...
4
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0answers
72 views

The reverse pizza problem .

The pizza problem is a fairly well-known problem which sounds like this : You have a circular pizza and you need to cut it such that you and your friend would both receive half of the pizza . ...
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2answers
41 views

Equality of two chords formed by intersections of circle with tangent lines to another circle [duplicate]

We have two circle C(O,OC) and C(Q,QA). We know that AO and BO are tangent for C(Q,QA) and QC and QD are tangent for C(O,OC). We want to prove that LJ = KT. Is it possible to help me?
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3answers
52 views

Circle and a line that passes through it

Given a line with equation: $y=ax-3$ that passes through a circle with equation $(x-1)^2+(y-1)^2= 1$. Find the range of values of $a$. I tried graphing and got: $0<x<2$ and $0<y<2$. I ...
1
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3answers
38 views

Placing a small circle within a large one, trying to maximize the circumference converage

Assume you have a circle of radius $1$. We want to place a smaller circle of radius $r<1$ inside, such that as much of the outer circle's circumference is contained inside the smaller one's area. ...
0
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3answers
54 views

How to know if a given point is inside a 2d circle's segment

This is for a real life situation not a theoretical one. I'm trying to check if a point exist in a Segment of a 2d circle. In other words, I need to know if a given point P(x,y) is anywhere inside the ...
1
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1answer
37 views

Question on circles geometry [closed]

The circle ω touches the circle Ω internally at P. The centre O of Ω is outside ω. Let XY be a diameter of Ω which is also tangent to ω. Assume PY > PX. Let PY intersect ω at Z. If Y Z = 2PZ, what is ...
1
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1answer
27 views

Rewrite the equation $(x-a)^2 + (y-b)^2 = r^2$ to make $y$ a function of $x$

I'm trying hard to figure out how $(x-a)^2 + (y-b)^2 = r^2$ can be written as $y = b + \sqrt{r^2 - (x-a)^2}$. My book says that you’ll want to have $y$ as a function of $x$.
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0answers
46 views

Find if a point is inside this part of the 2d circle.

How do you prove or disprove that a point P(x,y) is inside part of the circle. that takes up a shape of a pie? And, the pie can vary in size. Please see image link for example. The only known values ...
1
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1answer
23 views

Appolonius three circles problem, finding centre of tangent circle (analytic geometry)

Given 3 circles: $C_1$ centered at $(0,0)$ with radius 1 $C_2$ centered at $(a,0)$ with radius $a+1$ $C_3$ centered at $(-a,0)$ with radius $a+1$ (so $C_1$ is internaly tangent to both $C_2$ and ...
1
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1answer
23 views

Change multiple positions of points on circles with different radius

There are some points which are placed on a circular path: Now I want to change the position of some points equals to the distance value(d) respected to their path. I'm using this formula to ...
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1answer
31 views

Product of the Radii

$A_1$ and $A_2$ are two circles in a plane. The common external tangent to $A_1$ and $A_2$ consists of length $2017$. The common internal tangent consists of length $2009$. Find $r_1 \cdot r_2$ the ...
0
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0answers
59 views

Circle around three given circles

Given three arbitrary, non-overlapping circles, I need to find the smallest circle that encloses all three circles. I need a formula for the non-trivial case, where the enclosing circle touches all ...
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0answers
22 views

Circle homography

I'm attending a 3d-graphics course and I want to figure out which homograpic transformations conserve a circle's equation. The circle's equation is given as: Circle = $x^2 + y^2 + Ax + By + C = 0 $ ...
2
votes
1answer
28 views

How do I calculate the distance from point A from point B?

I've got this drawing of a circle, and I'd like to know how I can calculate the distance between point A to point B in a straight line. I already have: Radius: 100 Arc length: 78.5 ...
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1answer
50 views

Find the Area of the circle inscribed in a square.

Objective:To find r and area of the circle inscribed in a square, when two parameters are given.
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3answers
41 views

Find the length of common chord of two intersecting circles

Let us consider two intersection circles $x^2+y^2+2g_1x+2f_1y+c_1=0$ and $x^2+y^2+2g_2x+2f_2y+c=0$. Then equation of common chord of the above two circles is ...
0
votes
1answer
48 views

Find the ratio of the radii

Euclid Contest April 2015 Problem 8B I cannot type it as it has a diagram along with it, which might mess up my interpretation. This was a tough problem, I cannot solve it completely. HINTS ...
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1answer
38 views

geometry question on circles $C_1$ and $C_2$ with following conditions

Two circles $C_1$ and $C_2$ in the plane intersect at two distinct points $A$ and $B$ , and the centre of $C_2$ lies on $C_1$. Let points $C$ and $D$ be on $C_1$ and $C_2$, respectively, such that ...
0
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1answer
29 views

Family of circles, maybe?

Circles are drawn passing through the origin O to intersect the coordinate axes at points P and Q such that $(m)(OP)+(n)(OQ)=k$, then the fixed point satisfying all such circles is? (A) ...
0
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1answer
19 views

Power of a point with respect to a circle

I was reading the power of a circle from this-http://mathworld.wolfram.com/CirclePower.html Here they are saying tht the power of A with respect to the circle of radius r is given by $p= AP \times ...
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1answer
36 views

Given coordinates find triangle and circle intersections

For example we have a circle and triangle. We need to check if at given $(m, n)$ coordinate triangle is intersecting with circle (area). Circle center is fixed at $(100, 100)$ with radius $R = 50$. ...
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2answers
32 views

Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.

The question is as follows if $ABC$ is a triangle, with $AD$ as the internal angle bisector of $\angle A$ with $D$ at $BC$ and $B^{'}, C^{'}$ are reflection of points $B$ and $C$ in $AD$. Show that ...
0
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3answers
69 views

Find the area and perimeter of shaded region.

(a) Find the area of the shaded region. (Round your answer to one decimal place.) (b) Find the perimeter of the shaded region. (Round your answer to one decimal place.) $\qquad \qquad \qquad \quad$ ...
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4answers
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The “pepperoni pizza problem”

This problem arose in a different context at work, but I have translated it to pizza. Suppose you have a circular pizza of radius $R$. Upon this disc, $n$ pepperoni will be distributed completely ...
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2answers
25 views

3D shape with orthogonal projections that form circles of the same radius.

Let's say you have a 3D shape. The side view, front view, and top view of the shape are all circles of the same radius. Does the shape have to be a sphere, or is it possible that it could be another ...
0
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1answer
22 views

Equation of a Circle (Complex Eq.)

I am working through a calculation and it says that when $\omega$ is close to $\omega_L$, the second term below describes a circle with a diameter of $d = \frac{2 \kappa}{1 + \kappa}$. Can someone ...
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2answers
75 views

Area of a Triangle Inside a Circle?

I have a circle of radius $r$ and a triangle inside that circle. Specifically, if you have the triangle $\triangle ABC$ inside a circle with only the one side $AB$ and an angle $\angle \text{B}$ ...
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0answers
22 views

Analyzing angles in Excel

I have linear data points in Excel that represent vectors on a polar plot. I would like to use the slope of these vectors to give me the angle of this vector. I have used this equation to find the ...
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0answers
13 views

Contour lines/map of a function

I have the function f(x,y)=exp(-x^2-y^2) I have no idea how to find the center of the circle and the radius. I know the formula is ...
0
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1answer
67 views

Locus of centres of circles tangent to two fixed circles?

Find the locus of the centres of circles tangent to two fixed circles. From my initial observations, I strongly think that the locus may be part of a hyperbola or some other conic? (because the ...
1
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1answer
34 views

Family of Circles

A system of Circles pass through $(2,3)$ and have their centers on the line $x+2y-7=0$. Show that the chords in which the circles of the given system intersects the circle $S_1:x^2+y^2-8x+6y-9=0$ are ...
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1answer
29 views

What are all of the points around a circle? Is there a formula provided degree rotation to find a given point?

I have a camera in 3-space which I want to spin around the y-axis. The distance remains the same, but the x- and z-positions change. The above is the direction I need to rotate. It's a top-down ...
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3answers
27 views

Finding center of circle from 3 coordinates

How would I solve this question (from the SAT): In the coordinate plane,the points $F (-2,1)$, $G (1,4)$, and $H (4,1)$ lie on a circle with center P. What are the coordinates of point P ? ...
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0answers
37 views

Fun Q3: So many circles! Find Test's area

A circle of radius $r$ is drawn at the center $O$. Two lines are drawn. Horizontal line which intersects the circle at point $A$ line angled $0 \leqslant \theta \leqslant 180$ from the horizontal ...
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2answers
46 views

Finding Area of a triangle inside a semi circle.

I'm familiar with basic high school trig. The answer is $2\sin(\theta)\cos(\theta)$. I'd appreciate it if someone could give me an explanation.
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0answers
11 views

scan a box in a circular manner..

I am the moment trying to figure out an expression that is capable of giving my what elements lies in a 2d array, when it is looked at from the center at certain angle out. for instance this is for ...
2
votes
2answers
78 views

Using deductive reasoning to determine what is wrong with this diagram

In this diagram the center of the circle is A, m∠ABD=20° and m∠DCA=52°. What is wrong with this diagram? I know that: m∠ABD=20° -given m∠DCA=52° -given AB∥DC -given (from image) AB≅AC≅AD -all ...
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2answers
89 views

Find the area of the region that lies inside the first curve and outside the second curve. $r = 10 \cos\theta,\ r = 5$

I am not sure of my answer. In the figure, $r=10 \cos\theta$ is a circle that doesn't look like a circle. The area of $r=5$ is $\pi r^2 = 25 \pi$. You remove the area from $-\pi/3$ to $\pi/3$ of ...
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2answers
39 views

Find probability distribution - choosing points from a circle

From a disk R we choose a point. Let X denote distance between chosen point and circle's centre. Find distribution of a variable $X^2$. I have no idea what should i do about that whatsoever so i would ...