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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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 ...
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1answer
283 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 ...
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1answer
314 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!
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343 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 ...
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2answers
43 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 ...
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2answers
123 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?
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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 = ...
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518 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 ...
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2answers
7k 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 ...
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1answer
324 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 ...
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53 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 ...
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2answers
1k 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 ...
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1answer
488 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 ...
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1answer
499 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 ...
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36 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 ...
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2answers
447 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 ...
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1answer
96 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 ...
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205 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 ...
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3answers
260 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?
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279 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 ...
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1answer
65 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 ...
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3answers
89 views

Find the locus of $2/z$ given that $|z-(1+i)| = 2$

If complex numbers $z$ satisfy the equation $|z-(1+i)| = 2$ and $\displaystyle \omega = \frac{2}{z}$, then locus traced by $\omega$ in complex plane, is ... My try I want to solve it ...
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2answers
597 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 ...
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1answer
422 views

Problem of a circle tangent to three other circles [closed]

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 ...
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1answer
238 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
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99 views

Finding three collinear points passes through three circles

Assume that we have three collinear points $A(x_0,y_0),B(x_1,y_1)$ and $C(x_2,y_2)$. They are on three different circles whose centres and radii are respectively $\big((P_x, P_y), r_P\big)$, ...
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1answer
120 views

Finding the side lengths of a rectangle given a circle passing through one of its vertices and touching two of its sides

A circle touches a rectangle $ABCD$ of side lengths $2a$ and $2b$ at $M$ and $N$ on sides $AB$ and $AD$ respectively. It also passes through the point $C$. If the perpendicular distance of the line ...
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1answer
25 views

What does the locus of $M$ form?

Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, what does the locus of ...
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55 views

Complex Number and Geometry

Given $A(3+4i)$, $B(-4+3i)$ and $C(4+3i)$ be the vertices of a triangle $ABC$ which is inscribed in a circle $S=0$. Let $AD, BE, CF$ be altitudes through $A, B, C$ which meet the circle S=0 at ...
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1answer
167 views

Crazy rectangles, semi-circles, and circles!

Problem is to find the ratio of the area of the circle to that of the semi-circle. Note that points $F$ and $E$ weren't given in the original diagram, and that the circle at the top-right ...
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1answer
118 views

Horses grazing in a circle.

Question: Diagram: Note that The circle with center $C$ is touching the arc of semi-circle $AB$ also; I couldn't draw it. The figure wasn't drawn on cartesian planes; so, though it may seem ...
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63 views

Locus of the centre of a circle $\Gamma$

Let $\Gamma_1,\Gamma_2$ be two circles centred at the points $(a,0),(b,0);0<a<b$ and having radii $a,b$ respectively.Let $\Gamma$ be the circle touching $\Gamma_1$ externally and $\Gamma_2$ ...
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1answer
43 views

Determine the length of **DC** in terms of $l_1$ and $l_2$

In the given figure, E is the midpoint of the arc ABEC and ED is perpendicular to the chord BC at D. If the length of the chord AB is $l_1$, and that of BD is $l_2$, determine the length of DC in ...
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2answers
163 views

Finding the angle between the $2$ radii of a circle

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 what is the value of ...
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2answers
74 views

Interior point of $\Delta\,ABC$

if $P(\lambda,2)$ is an interior point of $\Delta\,ABC$ formed by the lines $$x+y=4$$ $$3x-7y=8$$ $$4x-y=31$$ Find $\lambda$ My Idea: The vertices of $\Delta ABC$ are $A(\frac{18}{5},\frac{2}{5})$ ...
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1answer
431 views

Circumcircle of an isosceles triangle and length relation

I was asked to prove the following problem. Consider the following diagram where a triangle $ABC$ lies inside its circumcircle, $D$ is the point where the angle bisector $\alpha$ of $B$ intersects ...
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1answer
50 views

is diffrence of raduis of 2 circles is not depend upon thier peremeter

I read on the Internet it's true, but I suspect it: Image describing the puzzle Take a ribbon tightly wound around the equator of the earth. Add 1 meter to that ribbon by cutting it at any ...
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2answers
27 views

Determine if circle contain point ( geographic ) while the number before the point are equals

I want to check if circle contain some point(latitude and longitude). the problem I have is that the number before the point are equals, for example: ...
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1answer
361 views

Formula to calculate a side of triangle with given angle

I have triangle like in the picture. The known angles: α (total angle of the I-J-K2 triangle) b (total angle of the I-P2-K2 and I-P1-K2 triangles) The known 3D points with X,Y,Z-coordinates: ...
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0answers
463 views

Family of circles touching a line

I found this in a book but I am not able to understand how they got this result. It goes the equation family of circles touching a given line $(y-y_1)=m(x-x_1)$ at $(x_1,y_1)$ for any value of $m$ is ...
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3answers
38 views

Graphing a Circle that doesn't have two of each variable

Graph the circle: $$x^2+y^2-2x-15=0$$ I know how to approach this problem if there were two $y$ and $x$ variables. But there is only one $y$ variable. How would I approach this?
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1answer
117 views

Finding a point on a circle that has a distance L (arc length) from another point

Given the coordinates of a single point on a circle and a length of an arc $L$, how do I find the coordinates of another point? Or, to put in another form: I have the radius $r$, the length of the ...
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1answer
352 views

Proof of “Japanese Theorem” — Triangulation of Cyclic Polygon

On Mathoverflow, I saw this great result on the "Japanese Theorem". “Japanese Theorem” on cyclic polygons: Higher-dimensional generalizations? Given triangulation of a cyclic polygon, the sum of ...
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210 views

Maximum speed in a circular orbit?

Visualize two points:  $O\equiv(0\mid 0)$ and $D\equiv(d\mid 0)$.  The two are $d$ units apart.  Visualize a movable rod whose endpoints, $C_O$ and $S_O$, are a unit apart. $C_O$ always coïncides ...
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2answers
717 views

How to find distance between two different circles

I am trying the find the distance between two different sized circles, both centred on the horizontal plane. I know the diameter of each circle, and the length around both circles if wrapped like a ...
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600 views

Find the two lines from a given slope that are tangent to a given circle

Guys please teach me how to solve this one. I want to learn. The question is find an equation of each of the two lines having slope -4/3 that are tangent to the circle x^2 + y^2 + 2x -8y - 8 = 0.
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Finding an equation of a circle with a given center and a tangent line.

My math homework is finding an equation of the circle. Given that the center is at (-3,-5) and tangent to the line 12x + 5y =4. I don't know how to solve this since our professor didn't teach this to ...
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1answer
100 views

Two circles intersection

Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is ...
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1answer
197 views

Two circle intersection [duplicate]

Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points?
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42 views

Possible to square circle using additional tools?

So I just stumbled upon the wikipedia page for squaring the circle and learned that it's impossible to do with only a straightedge and compass. Is this possible if we are allowed to use any other ...