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

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18
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6answers
735 views

Is this 3D curve a circle?

The following is a curve in $3$ dimensions: $$\begin{eqnarray} x & = & \cos(\theta) \\ y & = & \cos(\theta - \pi/3) \\ z & = & \cos(\theta - 2\pi/3) \end{eqnarray}$$ Is the ...
2
votes
4answers
829 views

Extending the length of a curcumference by 1 meter

I once heard the following statement: Take a piece of string and measure the length around a ball. Now add 1 meter to the string and stretch it out evenly around the ball. Obviously the ...
3
votes
2answers
167 views

Savings when driving the inside edge of a curve.

I was wondering how many kilometers/meters I would save if I always drove on the inside edge of the curves between my home and workplace, compared to driving in the middle of the lane. If the lanes ...
3
votes
1answer
138 views

Circle Acting on Circle/Ball

Is much known about $S^1$-actions on the following simple spaces?: 1) $D^2$ the disk 2) More generally $D^n$ the n-ball 3) $S^1$ the circle In particular, does every $S^1$-action on the disk (or ...
0
votes
1answer
402 views

How to find the intersection of union of two circle groups

I have two groups of circles. S1 is the union of the first group and S2 is the union of the second group of circles. I know center and radius of all circles. I have to find the equation for the ...
1
vote
1answer
2k views

Calculate using cross-section of tunnel

http://imageshack.us/photo/my-images/545/88060057.png/ The figure shows the cross section of a railway tunnel. The radius of the tunnel is $3.5$m, i.e $OA = 3.5$m. $\angle AOB=90^\circ$. Calculate ...
1
vote
1answer
1k views

Find distance traveled by tips of hands of clocks?

The short and the long hands of a wall clock are $8$ cm and $12$ cm respectively. Find the sum of the distance traveled by their tips in $3$ days. Give your answer in terms of $\pi$. My ...
0
votes
1answer
535 views

Circular Sector to Circle Intersection

Is there a formula for determining if a sector intersects a circle (as well as determining if the circle/sector are inside each other)? Sector definition: A center point $P(x,y)$, a starting angle in ...
1
vote
1answer
186 views

A calculation involving two circles

I have two circles, one of which is completely within the other. They do not touch, but are not necessarily concentric. I am given the sum of their circumferences, and the difference in their areas ...
1
vote
1answer
632 views

Geometry Puzzle - Largest circle on Chess

The following puzzle was asked in company interview round.I have no idea ,how to do it? ...
1
vote
2answers
1k views

Formula for calculating the center of an arc

Is there a formula for calculating the point equidistant from the start point and end point of an arc given: 1) An arc is defined as: A center point $P$, a radius $r$ from the center, a starting ...
1
vote
2answers
420 views

A circle on the plane [duplicate]

Possible Duplicate: Parametric Equation of a Circle in 3D Space? I know that, for example, if a circle is on a plane with counter-clockwise orientation, and with center $(a,b)$ and radius ...
2
votes
3answers
78 views

From the given arc is known the start point the end point and a random point on the arc how we can find the center point coordinates?

From the given arc is known the start point the end point and a random point on the arc how we can find the center point coordinates?
0
votes
2answers
6k views

About Perimeter - Circumference of Quarter Circle

ASB is quarter circle. PQRS is a rectangle with side PQ=8 and PS=6 . What is length of ARC AQB ? Ans $5\pi$ Here is how I am solving it: Radius of Quarter circle = diagonal of ...
0
votes
1answer
854 views

Find the coordinates of a point on a circle given 2 points and an angle

I have a circle with A as a center, B and C 2 points on the circle. I have the coordinates of A (the center) and B (the point on the circle). How can I find the coordinates of C (another point on the ...
5
votes
2answers
1k views

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept Like previously mentioned, I'm not all too familiar with circles. So, I plotted the ...
3
votes
4answers
2k views

Find center, radius and a tangent to $x^2+y^2+6x-4y+3=0$

For the circle $x^2+y^2+6x-4y+3=0$ find a) The center and radius b) The equation of the tangent line at the point $(-2,5)$ Now, I solved a) and got the equation $$(x+3)^2+(y-2)^2=10$$ with ...
0
votes
3answers
896 views

Triangle Inside Circle

If the radius of the circle is equal to the length of the chord $AB$, what is the value of $x$? How would I solve this problem ?
4
votes
1answer
292 views

Length of chord in circle - Which property

In the figure AB=4 , BC=6 , AC=5 and AD=6 what is length of DE ? Ans=9 I know there must be some property here that would solve this problem instantly but I cant figure it out any ...
1
vote
2answers
3k views

Area of Shaded Region

How would I calculate the area of the shaded region of a circle with radius 6 and length of chord AB is 6.
0
votes
1answer
248 views

clock related question

My question is- If the angle between the hour hand and the minute hand at 8 hours and x (>0) minutes is exactly 120 degrees then (11x - 200) equals? My solution is:40 I would like to know whether ...
0
votes
1answer
125 views

Radius by chordal length and segment area

Is there any formula to find radius of a circle segment if we know chordal legth and area of the segment?
0
votes
2answers
355 views

Calculating the points of tangency for two circles given a picture

I have two circles with the same radius and I want to calculate the points of tangency. For example, in the picture below, I want to calculate $(x_3, y_3)$ and $(x_4,y_4)$. I have the radius and the ...
0
votes
2answers
308 views

Solving a set of “circular” quadratic equations

$x_a'$ and $y_a'$ are unknown. What's the simplest way to solve it? Every time I tried, it grew into tremendous size or was unable to think out in reasonable amount of time due to it's complexity. ...
6
votes
1answer
527 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
3answers
1k views

Area of a sector - Inscribed Angle and Central Angle

I know the formula for the area of a sector of an arc made by central angle is $$\text{Area}_\text{Sector}= \frac{\text{Arc Angle} \times \text{Area of Circle} }{360}$$ Now my question is , Is this ...
3
votes
3answers
384 views

Deteriming an angle without Trig. ratios

I am trying to solve the current problem If O is the center of a circle with diameter 10 and the perimeter of AOB=16 then which is more x or 60 Now I know the triangle above is an ...
3
votes
1answer
324 views

Find the radius of the smallest circle in terms of the side of the square.

The side length of the square is $a$. Two different quadrants are inscribed in it as follows. A small red circle is also inscribed between them. Find the radius of the smallest circle (red one) in ...
4
votes
1answer
149 views

Circular Rotation

I'm trying to emulate planetary rotation. I have a 'planet' rotating around the 'sun', but when trying to rotate the 'moon' around the 'planet', the motion is skewed. If I stop the motion of the ...
3
votes
3answers
2k views

Finding a point having the radius, chord length and another point

Me and a friend have been trying to find a way to get the position of a second point (B on the picture) having the first point (A), the length of the chord (d) and the radius (r). It must be possible ...
0
votes
1answer
158 views

Calculating Points in Circles

I am trying to calculate the points around a circle with a certain distance in between each other. Below is a graphical representation of what I am attempting to do. The diameter is 70 (radius 35), ...
2
votes
1answer
474 views

Trying to reverse engineer this pattern…

this is my first post on the mathematics node of stack exchange, so please forgive me if I'm not posting an appropriate question, but I'm not sure where else to address this. I'm trying to figure out ...
-2
votes
3answers
698 views

What will be the shape of circle if it has no pi (π) [closed]

I not so good with mathematics I like to know if there is no pi (π) existed in this world what will happen to a Circle. What will be the shape of it
1
vote
3answers
237 views

Diameter of wheel

If a wheel travels 1 mile in 1 minute at a rate of 600 revolutions per minute. What is the diameter of the wheel in feet ? The answer to this question is 2.8 feet. Could someone please ...
2
votes
6answers
13k 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?
2
votes
2answers
557 views

circles and linear fractional transformations

I'm realizing how little (in some respects) I know about circles. Here's something that emerged out of something I was fiddling with. My question is whether this is "well known" in the way that ...
3
votes
1answer
167 views

Can't understand this solution.

I came across a problem which was already present on the internet. If an arc with a length of $12\pi$ is $\frac{3}{4}$ of the circumference of the circle, what is the shortest distance between ...
3
votes
2answers
290 views

Angles of triangle inside a cricle

In the figure shown if area of circle with center o is 100pi and CA has length of 6 what is length of AB ? I looked around on the web and cant seem to get an idea of what the angles AOC ...
0
votes
1answer
125 views

rather simple question

This is probably an easy question but I don't get it. Please answer in a easy way :P Imagine you want to paint circles on a linear line. The line is 100cm long. On the right side you have a circle ...
3
votes
4answers
5k views

Polar equation of a circle

A very long time ago in algebra/trig class we did polar equation of a circle where $r = 2a\cos\theta + 2b\sin\theta$ Now I forgot how to derive this. So I tried using the standard form of a circle. ...
1
vote
2answers
62 views

rates of motion of projected points along a circle

Have I forgotten all my secondary-school geometry? (That's not actually my question.) Suppose $R>r>0$ and consider this circle (later edit: I think $R>0$, $r>0$ is enough; we don't ...
1
vote
1answer
712 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
2
votes
1answer
839 views

Finding points relating to the edge of a circle in an x,y coordinate system

My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
1
vote
1answer
266 views

Find a circle that is tangent to a line and a circle.

I need to find the circle that will be tangent to a line at a given point and a circle. The diagram below hopefully makes it clearer. The known data are: points P2,P3,P4,P5 Circle C2's radius r ...
2
votes
2answers
552 views

Connecting two tangents with two circles of equal radius

In a cartesian system I have 2 lines (an input and an output) and want to find the radius (r) and centre (c1, c2) of the two circles of equal radius that are touched tangentially at the end point of ...
5
votes
1answer
452 views

Rotation $x \to x+a \pmod 1$ of the circle is Ergodic if and only if $a$ is irrational

I have a book, Ergodic problems of classical mechanics by Arnold/Avez, and in it they prove that rotation $Tx = x+a \pmod 1$ of the circle $M=\{x \pmod 1\}$ is Ergodic if and only if a is irrational. ...
2
votes
3answers
1k views

3-D equation of a circle

I came across a sum but could not solve it as i dont know the 3d equations of a circle : The sum is If $A(3,-2,2)$ and $B(2,9,5)$ are the end points of a diameter of a circle,then the third pt that ...
1
vote
3answers
837 views

angle of an inscribed triangle

I have a scalene triangle inscribed in a circle, one of its sides $a$ is $2\sqrt3$ and the length $r$ from that side to the center is $1$. I need to find the angle $x$ opposite to the side given. ...
7
votes
1answer
1k views

How to turn this sum into an integral?

I have been trying to find the closed form of this sum to no avail. It was suggested to me to try and turn this sum into an integral and solve it like that. However, I am confused as to how to do ...
2
votes
1answer
283 views

Convergence and closed form of this infinite series?

If we have a circle of radius $r$ with an $n$-gon inscribed within this circle (i.e. with the same circumradius), we can find the difference of the areas using: $$A_n =\overbrace{\pi r^2}^\text{Area ...