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

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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 ...
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2answers
71 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, ...
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1answer
42 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 ...
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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 ...
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3answers
58 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
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1answer
61 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.
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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 ...
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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) ...
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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
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1answer
30 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
35 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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1answer
48 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
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 ...
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2answers
30 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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4answers
463 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
167 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
66 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
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 ...
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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 ...
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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 ...
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2answers
50 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
62 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
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 ...
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0answers
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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
53 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
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 ...
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0answers
21 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
143 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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3answers
121 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
16 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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2answers
44 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
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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 ...
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0answers
14 views

$L=R\alpha=R({H^4\over32R^4}-{H^2\over4R^2}-{1\over2})$

Let $XY$ be a diameter of a circular pond of radius $R$. A vertical pole of height $H (H < 2R)$ is erected at $Y$ . An observer at $X$ finds that the angle of elevation of the top of the pole is ...
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1answer
34 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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0answers
41 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 $\big((P_x, P_y), r_P\big)$, ...
0
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1answer
24 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 ...
0
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1answer
12 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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0answers
34 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
34 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 ...
2
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1answer
38 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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1answer
20 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 $\Gamma_2$ ...
2
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1answer
20 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
47 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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0answers
16 views

How to compute an angle from arbitrary limits (min and max) and a default value?

My question is about a software problem but I think it's more related to Math equations. I'm developing a round knob which is limited to 315deg with a 45deg unused part of the knob. I have some ...
2
votes
2answers
27 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 $A(\frac{18}{5},\frac{2}{5})$ ...
3
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1answer
76 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 ...
3
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1answer
32 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
21 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
58 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
43 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 ...