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

learn more… | top users | synonyms

3
votes
1answer
48 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 ...
0
votes
1answer
133 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:
0
votes
1answer
68 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
vote
1answer
37 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 ...
0
votes
2answers
40 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 $a = (1 + \sqrt{2})b$
0
votes
2answers
54 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
vote
1answer
44 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
votes
3answers
50 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 ...
1
vote
1answer
64 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
votes
1answer
18 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 ...
0
votes
1answer
78 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
votes
1answer
30 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???
0
votes
3answers
38 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
vote
1answer
85 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
vote
1answer
48 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
63 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
95 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
votes
1answer
44 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
vote
2answers
84 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
votes
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
votes
1answer
107 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
68 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
votes
2answers
48 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
vote
4answers
179 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
79 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. ...
2
votes
2answers
74 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
vote
0answers
92 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
34 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
51 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
vote
3answers
35 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
votes
3answers
59 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
42 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
119 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
63 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
53 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
votes
2answers
26 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?
0
votes
2answers
26 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, -15) 4) ...
1
vote
2answers
43 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 ...
1
vote
3answers
63 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
votes
3answers
78 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 ...
1
vote
2answers
38 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 = ...
0
votes
1answer
45 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 ...
2
votes
2answers
40 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 ...
1
vote
4answers
71 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 quadrilateral ABCD. ...
0
votes
1answer
57 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 ...
0
votes
3answers
42 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),...
1
vote
2answers
81 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?
1
vote
2answers
50 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 ...
1
vote
1answer
36 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.
3
votes
2answers
61 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 ...