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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1answer
40 views

Points of intersection between circle and parabola

Find the points of intersection between circle and a parable: circle: $x^2 + y^2 - 2x + 4y - 11 = 0$ parable: $y = (-x^2+ 2x + 1 - 2\sqrt{3})$ I don't understand how to solve this, I really tried, ...
0
votes
1answer
30 views

x(u,v), y(u,v), z(u,v) parametric equations for a special cycloid

I'm trying to find out a 3d parametric equations for a cycloid I know that a cycloid is a 2d curve it is generated by a point on a rolling circle. but my circle is rolling around another circle both ...
2
votes
2answers
46 views

If $ax + by = c$ is tangent to the circle $x^2 + y^2 = 16$

Problem: If $ax + by = c$ is tangent to the circle $x^2 + y^2 = 16$ then which of the following is correct option (A) $16 ( a^2 + b^2) = c ^2 $ (B) $16 ( a^2 - b^2) = c ^2 $ (C) $16 ( a^2 +b^2) = - ...
2
votes
1answer
37 views

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through the points $(1,0)$ and $(3,0)$ and touches the circle $x^2+y^2-2x-8=0$ and have its ...
1
vote
1answer
31 views

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r.$.

Consider a series of n concentric circles $c_1,c_2 \cdots c_n$ with radii $r_1,r_2.\cdots r_n$ satisfying $r_1>r_2>r_3 \cdots r_n$ and $r_1=10$ The circles are such that the chord of contact of ...
1
vote
0answers
19 views

The Biggest Smallest Piece to Smallest Biggest Piece ratio of a circle cut by n chords with maximal number of regions

It is well known that a circle cut by n chords gives at most (n^2 + n + 2 )/2 regions eg. http://mathworld.wolfram.com/CircleDivisionbyLines.html Questions:- How close to equal area regions can we ...
0
votes
0answers
17 views

Area covered by multiple (possibly intersecting) circles on surface of sphere

I have a number of circles of same radius on surface of sphere (Google Maps API). I'm trying to calculate the total area covered by these possibly intersecting circles. My current solution is ...
0
votes
2answers
18 views

Circle touching three tangential circles

The circles $C_1,C_2$ and $C_3$ with radii $1,2$ and $3$, respectively, touch each other externally. The centres of $C_1$ and $C_2$ lie on the $x$-axis, while $C_3$ touches them from the top. Find the ...
1
vote
2answers
41 views

what is the difference between tangent and slope of tangent?

I need your help, my question is what is the difference between tangent and slope of tangent ? A clear example would be appreciated. Thank you.
0
votes
0answers
49 views

Circle in a triangle, tangent to two sides and inscribed circle

I'm trying to use a greedy algorithm to solve Malfatti's problem: Malfatti's problem. I want to solve it for general (integer sided) triangles, and this is what I have done so far: Let a,b and c ...
1
vote
2answers
45 views

Find $\angle BOD$ in the given figure.

Consider a circle with centre $O$. Two chords $AB$ and $CD$ extended intersect at a point $P$ outside the circle. If $\angle AOC=43^\circ$ and $\angle BPD=18^\circ$, then the value of $\angle BOD$ is ...
0
votes
1answer
34 views

Finding the points of intersection of the circles [closed]

How can you find the points of intersection of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2+2x+2y-2=0$?
1
vote
2answers
39 views

Furthest distance between two circles in 3D

I have two circles in 3D specified by their centers, $c_1, c_2$, their radii, $r_1, r_2$, and the normals of the plane each circle is embedded in, $n_1, n_2$. Note that $n_1$ is not necessarily ...
1
vote
2answers
71 views

Calculating the arc length of a circle segment

I would like to calculate the arc length of a circle segment, i.e. I know the start coordinates (x/y) of the circle segment, the end coordinates (x/y) and the x and y distances from the starting point ...
4
votes
3answers
73 views

what does tangent mean?

I need your help, my question is what does tangent value mean and how can we benefit from it ? I know that $\tan(\theta) = \dfrac{\sin(\theta)}{\cos(\theta)}$, but what does that mean? Sorry I am ...
2
votes
0answers
56 views

To find a fifth degree equation by using circles and lines that cannot be solved by radicals

An example quintic whose roots cannot be expressed by radicals is $x^5 - x + 1 = 0$. I asked a geometry question about a fifth degree equation long time ago . I had an equation in the question. It ...
3
votes
1answer
317 views

How many points does 'the-most-point-contained-circle' contain at least?

Question : Letting $n\ge 2\in\mathbb N$, how can we find $f(n)$ such that the following two propositions are true? If finding $f(n)$ is difficult, then how can we find 'good' function $g(n),h(n)$ ...
0
votes
3answers
45 views

Find the point in the circle

The circle $C$, given by the equation: $$x^2 + y^2 + (1+k)y - (k+1) = 0 $$ pass through the same two points for every real number $k$. Find the coordinates of these two points. Find the minimum ...
4
votes
4answers
138 views

A problem on circle

Consider a circle $C$, such that $\overline{AB}$ is a chord. $P$ be a moving point on the circumference of the circle. (i) How to find the point $P$ such that $\overline{PA}\cdot \overline{PB}$ is ...
1
vote
2answers
76 views

Circle areas on squared grid

There is a circle. On 9 equal squares. Every square has some value assigned to it. Every square gets weight, depending of what percentage of it is circle (area-wise). I need to find circle radius, ...
3
votes
1answer
45 views

Find Area of 3 Sector Circle, Variable center point

I have a Circle separated into 3 sectors. At start each sector has the same central angle, 120°. Therefore each sector should be taking up the same area. I want to be able to move the center point ...
4
votes
0answers
62 views

Does $T$ map a circle to a circle?

I have something to ask about the following map on in $\mathbb{C}$ $$ T \quad : \quad \longmapsto \frac{-2}{\bar{z}+i} -i $$ The map is well-defined whenever $z \neq i$. I have shown that it maps the ...
0
votes
3answers
59 views

Find how far runners travel on a circular track (trig)

-How far has each runner traveled after 8 seconds? Though I just had to convert the rad/sec to rev/sec to get yards then multiply that by 8 seconds, but that isnt correct. Find the angle θ, in ...
2
votes
1answer
66 views

Packing circles into circle of diameter 7

How many unit circles can you fit inside a circle of diameter 7 such that no circle overlaps any other circle? Please explain the concept or any tricky process regarding this problem.
0
votes
0answers
53 views

Technically speaking, how many sides does a circle have? [duplicate]

I know this question may not be logically coherent but, assuming that it is, how many sides does a circle have: zero or infinitely many? My intuitions have proven totally useless in trying to answer ...
1
vote
3answers
140 views

Tangents of circles

I'm trying to solve the following problem: Find the tangent equations of $x^2 + y^2 = 1$ which pass though point $(1, 2)$. As a line which goes though the point $(1, 2)$ is in the form $y = m(x - 1) ...
0
votes
1answer
60 views

Equation of a star

About three years back I read an article in wikipedia about equation(it was more like how to draw a curve that remembled a star) of a star. Though I dont remember vividly in that article there was a ...
2
votes
1answer
31 views

Circle theorem/triange angle question

I am doing practise papers and there is one question I cannot understand even with the mark scheme. I have added the pictures below: Question (with added annotations): Mark scheme: The question ...
0
votes
1answer
36 views

Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
0
votes
1answer
49 views

Circle-circle intersection

In this article, two intersection points of three spheres are calculated. I want to reduce this solution to 2-D. How do I calculate the intersection points between 2 circles? I've tried to implement ...
1
vote
2answers
34 views

Determining points on a circle in a particular plane

This is more of a computer graphics question really, but I was just wondering the efficient way to determine n equally spaced points on a circle, given a normal vector to the circle and the radius of ...
1
vote
2answers
31 views

An ice cream cone is 8 inches tall and

An ice cream cone is 8 inches tall with a slant height of 10 inches . The opening of the cone is a circle.What is the diameter of the opening of the cone?
4
votes
4answers
478 views

How do I find the equation of a circle, given radius and centre coordinates?

Say I am asked to find, in expanded form without brackets, the equation of a circle with radius 6 and centre 2,3 - how would I go on about doing this? I know the equation of a circle is $x^2 + y^2 = ...
5
votes
2answers
175 views

Maximal area covered by two triangles in unit circle

What is the maximal area covered by two triangles in a unit circle? There are no restrictions other than that. They can overlap, touch the circle, not touch the circle etc. So far I have shown In ...
0
votes
2answers
71 views

Is it possible to find the domain and range of a circle function without graphing it?

If I am given a circle, such as, $(x + 1)^2 + y^2 = 9$, is it possible to determine the domain and range without having to graph it up? I know the answer, but I don't see any connection with that and ...
1
vote
1answer
28 views

Find Coordinates on a track

Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at the westernmost point of the track, and, at the same time, Alexandra started at the northernmost ...
0
votes
2answers
41 views

Finding coordinates on a circle

So this problem I am have difficulty with. I think where I am going wrong is how to calculate the initial theta. Do I just use pi/2 because in the pictures it show to angle theta off the 90 degree ...
0
votes
1answer
48 views

find degree of angle in given triangle [closed]

let us suppose that we have given triangle $ABC$,point $o$ is a center of circle in which this triangle is drawn,while point $I$ is point of center of circle ,which is drawn inside this triangle,it ...
0
votes
2answers
65 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 ...
1
vote
1answer
64 views

Area of intersection between 4 overlapping circles.

I'm having difficulties finding the are of a section on the 4th circle when 4 circles intersect. The circles have a diameter of 150 mm, and the centers of adjacent circles are 100 mm apart. The shaded ...
0
votes
1answer
62 views

Find angle in radians on a Ferris Wheel

John has been hired to design an exciting carnival ride. Tiff, the carnival owner, has decided to create the world's greatest ferris wheel. Tiff isn't into math; she simply has a vision and has told ...
1
vote
0answers
14 views

Trilateration question help

Kind of stuck n this question, I just got the circle equation written down for the robot don't know what to do from here. A bicycle robot is travelling on a circle centred at the origin and with a ...
1
vote
2answers
64 views

Finding the area of the shaded region on a circle.

So I need help finding the area of the shaded A region. I was going to do pi*(r^2)*(45/360) - (the area of the smaller triangle). I just dont know how to get the angle or the lengths of it. Is there ...
1
vote
1answer
54 views

Circle Geometry - Proving Question

Suppose $C$ is any point on a circle, above a diameter $AB$. $P$ and $Q$ are points on the minor arcs $\widehat{AC}$ and $\widehat{BC}$. Prove that $$\angle APC + \angle CQB = \frac32\pi$$ Currently ...
1
vote
0answers
26 views

arrange div elements in circle and square

I n number of divs which are arranged in a circle using javascript. Right now i set the dimension of each div to 40*40. Below is what i am able to achieve so far. This is how i find X & Y of each ...
0
votes
3answers
144 views

Sketching graphs of circles.

A circle graph function is in the form of $x^2 + y^2 = r^2$ If I am asked to graph $(x-2)^2 + (y - 1)^2 = 4$, do I have to solve for x and y to graph first?
5
votes
3answers
125 views

Alternative form of equation of circle?

In a problem set I was solving, one of the solutions used the equation of a circle in the form $$(x-h)^2 + (y-k)^2 + \lambda(ax + by +c) = 0$$ where, $(h,k)$ is any point on the circle $ax+by+c ...
0
votes
1answer
17 views

Bertrand paradox Random midpoint

http://en.wikipedia.org/wiki/Bertrand_paradox_(probability) The link above explains Bertrand paradox in probability. In "Random Midpoint method" Bertrand uses a concept that all chords whose ...
1
vote
2answers
53 views

Calculate center of circle tangent to two lines in space

Good afternoon everyone! I am facing a problem which is straining my memory of linear algebra. I have: Three points with known coordinates, forming a triangle in space. Let the coordinates be ...
2
votes
1answer
66 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 ...