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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2
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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 ...
0
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2answers
329 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 ...
1
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4answers
607 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
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. ...
2
votes
2answers
117 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
289 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
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 ...
0
votes
1answer
98 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
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 ...
2
votes
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 $x$ ...
1
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1answer
153 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
515 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) $20(x^2 - y^2)- 36x + 45y = 0$...
-1
votes
1answer
79 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 non-...
4
votes
0answers
160 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 ...
1
vote
2answers
52 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, ...
1
vote
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 ...
1
vote
3answers
156 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
275 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
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 = ...
0
votes
1answer
184 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
56 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
314 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 ...
0
votes
1answer
106 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
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3answers
71 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
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?
53
votes
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.
1
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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 ...
1
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1answer
46 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.
4
votes
2answers
158 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 ...
0
votes
1answer
95 views

Enlarge 3 Circles about the same factor to find the Intersect

I currently have 3 circles that not intersect at all. Like this: Now i would like enlarge the circles about the same factor to find the intersection of this three circles. I have tried following ...
0
votes
1answer
102 views

Convex optimization approximation

Consider the optimization problem $\mathcal{P}_0$ \begin{equation*} \begin{aligned} & \underset{x\in \mathbb{R}^2}{\text{minimize}} & & \left\| x-p \right\|^2 \\ & \text{subject ...
2
votes
0answers
107 views

What is the curve's name for the “reciprocal” equation of a circle?

The equation of a unit circle is $$(x-a)^2+(y-b)^2=r^2$$ When the origin $$(a, b)=(0,0)$$ the equation becomes $$y=(1-x^2)^{1/2}$$ Naturally when this equation is plotted on graph paper we get a ...
0
votes
2answers
79 views

Intersection of circle and ellipse

I'm looking for the points of intersection of a circle $x^2 + y^2 = r^2$ ($r$ is known, origin is $(0,0)$) and an ellipse $(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1$ ($a,b,x_0,y_0$ are known). ...
1
vote
1answer
199 views

Distance to the perimeter of a circle with given radius, distance traveled from origin, and direction

I am programmer by trade but am running into some trouble with a geometry problem. I basically want to start at the center of a circle, travel any distance within the radius, turn any direction, and ...
0
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1answer
590 views

Find area of shaded region in circle

I am working on this SAT question. Progress AD = 3 largest radius =3 second largest = 2
3
votes
2answers
1k views

Circle Line segment intersection

I have a circle with radius r and center $(c_x, c_y)$. I have a line segment $(x_1, y_1)$ and $(x_2, y_2)$ given $(x_2, y_2)$ is always a point inside the circle. I am trying to find the ...
1
vote
1answer
433 views

How to find the area of intersection of two circles using axiomatic geometry?

Problem: square(ABCD) is a regular square, and a circle touches internally in the square. Also, arc(BD) divides the square. Then calculate the area of the colored region. This question is easily ...
2
votes
1answer
283 views

Not understanding arc midpoint computation

I'm trying to find the midpoint of an arc, so I found this page wherein Gregory V. Akulov and Oleksandr G. Akulov describe the midpoint formula. I pasted the formula & description from the site ...
2
votes
4answers
241 views

Area of a circle sector

I have been given the following proportional relationship to derive the area of a circle's sector: $\large\frac{\text{ Area of the sector}}{\text{Area of the circle}}=\frac{\text{arc length}}{\text{...
1
vote
1answer
108 views

Work out center of a partial circle

If I have a small section of a circle, inside a square. I know the height and the width of the square and therefore the width and height of the arc, what would be the quickest (not necessarily the ...
3
votes
1answer
124 views

Unit circle can't be covered by one chart

I am hoping that someone can give me a proof showing why the unit circle cannot be covered by one coordinate chart, or a reference where I can find a proof.
3
votes
1answer
80 views

Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$?

We are on $\Bbb{R}^2$. Let $A_1,\cdots,A_n$ be $n$ points on the unit circle. Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$ ? ( of course I mean the distance here) ...
2
votes
2answers
298 views

Deformable circle from a cubic Bezier approximation

I plan to draw approximate circles using a piecewise cubic Bezier representation. The representation should use four Beziers and be defined by four interpolating control points (let us call them ...
1
vote
4answers
176 views

Circle - finding the equation

Question: Find the equation of a circle whose center is in the first quadrant; touches the x-axis at (4,0) and makes an intercept of length 6 units on the y-axis. I am getting a faint idea where to ...
1
vote
1answer
145 views

Can any vertex of an isosceles triangle represent the centre of a circle, and the base vertices represent points on the circumference of that circle?

This question occurred to me doing this circle geometry problem, and I was wondering if anyone could clear it up. Geometrically, it seems it would make sense, provided that 2 sides are equal (equal ...
1
vote
1answer
53 views

Outer interval of circle intersection

Is there a consistent way to calculate the outer interval $\left(~\mbox{element of}\ \left[0, 2\pi\right]~\right)$ of a circle created by an intersection ?. I calculated the intersection points and ...
2
votes
2answers
270 views

Finding the position of a moving point [closed]

A point is moving on a given curve. For example, curve equation is: $$x^2 + y^2 - 10y = 0,$$ which is a circle with $5$ meter radius. If point is on $(0,0)$ at $t = 0$ and is moving on the curve ...
0
votes
3answers
2k views

Finding formula for an arc of a circle that fills a rectangle

I'm working on a program where I need to draw an arc in a rectangle fulfills these requirements: 1) The arc must be part of a perfect circle (not the band!), must not be oval 2) The arc intersects ...
1
vote
2answers
32 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
0
votes
1answer
354 views

Coordinate Geometry of circles; Radical Axis 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 at $(2, 1)$, then the radius of the second circle is? Apparently the solution is $3$, with the cryptic ...