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

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3
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3answers
50 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
3
votes
3answers
1k views

Area Between Three Circles of Differing Radii

From the link in wikipedia http://web.gnowledge.org/wiki/index.php/Area_Between_Three_Circles_of_Differing_Radii OPEN QUESTION: What is the equation, in three variables, relating the radii of ...
2
votes
1answer
36 views

Deriving angle from sin or cos

How can I derive the value in degrees of an angle starting from either the cos or sin value? $$ \cos(t) = c_{1} \quad \text{or} \quad \sin(t) = c_{2} $$
-5
votes
0answers
22 views

Find the area of the shaded portion in the circle. [on hold]

AC=28 cm Find the area of the shaded portion. EDIT: I have found out the area of the lower semi-circle I'm not being able to find the area of the upper half.
0
votes
0answers
20 views

Vector for arcs in path

I have path created from lines and arcs. I want to create next path inside or outside of this given path with given offset. For line I calculate line equation and it gives me simple perpendicular ...
0
votes
2answers
27 views

Intersections of two parabolas given focii

As part of Voronoi's algorithm, I need to calculate the intersection of two parabolas to compute a breakpoint at run time. I've spent literally 8 hours on this, and I've only gotten my equations to ...
0
votes
1answer
30 views

Finding the angle value given 1 point and the centre of a circle

I got the coordinates of the center of a circle $(a,b)$ as well as one other point $(x, y)$. From those I can derive the radius by applying square root to the result of following formula. $$ (x-a)^2 ...
1
vote
1answer
91 views

Finding the points of intersection of a circle and a line

In a test (of math in arabic language) we we're asked to find the points of intersection of a circle and a line. Their equation is given. In the test I solved system of equations made of their ...
2
votes
1answer
85 views

Problem of a circle tangent to three other circles

Two circles with centres A and B and radii 14 and 7 units respectively touch each other externally. M is the mid point of segment DE and is the centre of the circle with radius 21 units. The two ...
2
votes
1answer
97 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 ...
0
votes
0answers
29 views

Coloring a circle

A circular spintop is colored in blue, red and green. Whenever the spintop is rotated 120 degrees, the pattern of colors looks exactly the same, only that blue becomes red, red becomes green and green ...
37
votes
3answers
2k views

Cutting up a circle to make a square

We know that there is no paper-and-scissors solution to Tarski's circle-squaring problem (my six-year-old daughter told me this while eating lunch one day) but what are the closest approximations, if ...
1
vote
1answer
32 views

Find part of segment between two circle centers

I drew the following image to help me explaining the question: Having two circles Source and Target, I want to build an arrow like in the image. The Source has coordinates $Source(sx, sy)$ and ...
2
votes
0answers
43 views

A question concerning radians and arc length

I was asked by a colleague yesterday about how the formula for the arc length of a circle is derived. I wanted to give them a correct answer, so I said I'd get back to them once I'd thought about it ...
2
votes
1answer
44 views

Finding the radius of a third tangent circle

Sorry if this is a foolish question, but I'm having difficulty understanding how to solve for $r_3$ in the following diagram... According to WolframAlpha's page on tangent circles, the radius of ...
0
votes
1answer
20 views

The vertical projection of a chord of a circle?

I was wondering if anyone could help me with the problem below (finding x): So we are given t_i (the initial tangent angle to the circle), t_o (the exiting angle of the tangent of the circle), the ...
1
vote
1answer
19 views

Truncated geometric progression on the complex unit circle - how to minimize the maximum real value

Let $a = \text{e}^{i 2 \pi k}$, and let $n$ be a natural number. Then I have a set defined as follows: $S = \{ \text{Re} (a), \text{Re} ( a^2 ), \ldots, \text{Re} (a^n) \}$ I want to minimize $T = ...
0
votes
2answers
398 views

Find points on a circle given arc length and radius.

I am trying to layout a circle, given the arc length l, radius r and center (cx, cy). I need to find all the n points that are on the circle. What I've tried so far: The first part is to find n: n ...
2
votes
1answer
43 views

Requiring a Geometrical proof

In the figure, ABCD is a square circumscribing a circle ($\pi_1$) whose center is E, the point of intersection of the diagonals AC and BD. With A as center, AB as radius, sector ABD is drawn cutting ...
0
votes
1answer
31 views

How do I correctly measure the circumference of a circle

I found How exactly do you measure circumference or diameter? but it was more related to how people measured circumference and diameter in old days. BUT now we have a formula, but the value of PI ...
2
votes
1answer
294 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
0
votes
2answers
43 views

Finding whether the quadrilateral is cyclic or not

Is a quadrilateral with sides lengths $3$, $3$, $4$, and $4$ cyclic? Progress I found that sides joining 3 and 4 are of equal length. then I found that other diagonal should also have same length ...
8
votes
1answer
105 views

Is a line just an infinitely large circle?

A line is infinite, right? Well, if $-\infty = \infty$, then a line is an infinitely large circle. (Does this have something to do with $1/0$?) It seems wrong, is it? Could I disprove it? How ...
0
votes
2answers
39 views

Sine on a Circle

I'm walking a quarter mile circular walking track. The width of the track is 8 feet across. If I walk from one side of the track to the other, walking a sine wave that has a 20 foot period, how much ...
7
votes
3answers
20k views

How do I calculate the intersection(s) of a straight line and a circle?

The basic equation for a straight line is $y = mx + b$, where $b$ is the height of the line at $x = 0$ and $m$ is the gradient. The basic equation for a circle is $(x - c)^2 + (y - d)^2 = r^2$, where ...
3
votes
2answers
113 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
votes
1answer
11 views

Simple Angle from X and Y Axes Input

I am trying, given the position along the $X$ and $Y$ axes from a controller, where the positions range from $-1$ to $1$ ($1$ being up on the Y and right on the X) to convert this to the direction of ...
0
votes
1answer
38 views

How many ways can we place two types of balls on a circle?

There are $a$ red balls and $b$ blue balls, and I have to place all of these balls on circumference of a circle. The balls with the same color are indistinguishable. I thought the answer would be ...
0
votes
4answers
27 views

Finding the equation of a circle given one point and radius

What is the equation of the circle which passes through the point $(0,2)$ with radius $4$ and whose center lies on the line $y = x$?
0
votes
1answer
33 views

Drawing lines from tangents from two circles on both sides.

I need to draw two red lines connecting the tangents from two circles on both sides. I need an algorithm that would get them based on any angle these circles are in relation to another. I need the ...
0
votes
1answer
29 views

What is the radius of a circle tangent to two lines with a known angle between them

Given angle, $\alpha$, and distance, $d$, what is the radius, $r$, and angle, $\theta$, in the image below in terms of the known quantities?
0
votes
1answer
18 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
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vote
0answers
33 views

How to calculate the height of a segment based on radius and area

I'd like to calculate the height of a segment based on the area. I have the radius of the circle, the area of the segment and need to calculate the height of the segment. I found the following ...
3
votes
3answers
64 views

Find equation of a circle

Find equation of a circle passing through $(1, 1)$ and touching the circle $$ x^2 + y^2 + 4x - 6y - 3=0 $$ at the point $(2, 3)$. I am stuck as I cannot find more than $2$ equations for $3$ unknowns. ...
0
votes
1answer
25 views

How to find circumference origin position?

I need to find origin of circumference which is defined by two points and vertex angle of isosceles triangle: I've got radius of triangle by ...
0
votes
3answers
24 views

Express angular position of the Earth as a function of time

Say I have for example the Earth orbiting the Sun (in circular orbit) and I want to express angular position (in radians) as a function of time. Would I be correct in thinking that $2\pi/t$ does the ...
0
votes
0answers
28 views

Dense packing of circles in unit circle, matlab code

I'm having real difficulties with a packing problem: Given M circles with equal radius r, determine the maximum radius such that all the circles can be fitted into the unit circle, without overlap. ...
0
votes
2answers
47 views

Surface are of a lightbulb

I have this picture: How could I calculate the area of a "thing" in red square? It is a circle.
3
votes
1answer
719 views

Is *njwildberger* wrong about area and circumference of a circle?

In this video, njwildberger says that the area and circumference of a circle are proof-less theorems. But I heard that we can derive both the area and circumference of a circle using calculus? So are ...
10
votes
1answer
1k views

Proving collinear points

This problem is so hard that I cannot figure it out. I hope you guys can give me a small push on how to tackle this problem, as I have been thinking about this for, like a week. Here's the problem: ...
2
votes
4answers
9k views

How to prove that the tangent to a circle is perpendicular to the radius drawn to the point of contact?

I've tried drawing a parallel chord to the tangent but then how would you prove that the chord is perpendicular to the radius?
0
votes
1answer
26 views

Geometry: how to get the radius of a circle with just a chord of the circle

Answer: Able to find area with statement 1) The length of the segment AB is 10 Above are two statements asking whether I can solve for the shaded areas given the information they have provided. ...
3
votes
0answers
49 views

Problem about cyclic quadrilaterals

In cyclic quadrilateral ABCD, let E, F, G, H be the orthocenters of triangles BCD, CDA, DAB, ABC, respectively. Prove that EFGH is cyclic. Progress So far, found that if E is orthocenter of BCD ...
0
votes
2answers
72 views

Area+Pythagoras Theorem

In the figure below show that Area A + Area B = Area C. What is the answer to this question?
5
votes
1answer
471 views

Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
0
votes
1answer
25 views

Find a point on a cercle in an orthonormed system given an angle.

In this inverted orthonormed system, I need to find a formula that gives the x and y coordinates of a point on a circle in function of an angle A that have its top on the center of the circle. I know ...
0
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1answer
33 views

overlap between orbitting planets

If two objects are orbiting around a common center point with different velocities and at different radius. The point in time in which they are overlapping can be found out using their angular ...
0
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2answers
27 views

Finding Reference Angles in Precalculus?

I'm reviewing for an exam, and having some trouble with reference angles depending on the quadrant they lie in. For example, my book shows the following: I get the part about subtracting 12pi/6, ...
0
votes
1answer
34 views

Calculating the length of an arc

I am working on some simulation software, in which I have an entity that is spiralling around a particular point. As the entity starts spiralling around the point, and the radius of the spiral ...
1
vote
1answer
55 views

Counting regions in a disk that has been cut by lines

Let $n$ be a positive integer, and $n$ lines drawn in a ring such that each one of them intersects with all of them, but no more than two intersect at one point. prove that the lines cut the disk ...