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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How Do We Find Points On A Circle Equidistant from each other?

I'm a programmer and I saw this question on stackoverflow which exactly does my job: http://stackoverflow.com/questions/13608186/trying-to-plot-coordinates-around-the-edge-of-a-circle. In this, the ...
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1answer
89 views

Time based algorithm to make object orbit another in electron-type path?

I'm positioning an object in 3d space, and I want to make it orbit another object, in a semi-random electron-like orbit, such that it always stays the same distance from the origin. I can make it move ...
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0answers
75 views

How to calculate the fundamental group of $S^3$ without two linked cirles

I need to find: the fundamental group of the space obtained by cutting out the three-dimensional $S^3$ sphere of two circles, once linked with each other. Can you help me? I have no idea about it, i ...
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38 views

Need help finding algorithm to fix specified problem

First I want to say that I am not a mathematician, so asking a question in this area is not easy for me. So I will describe the issue in my words which is not the nice way. So this is what I do: I ...
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0answers
93 views

Prove three chords of a circle are concurrent iff their poles with respect to a circle are collinear.

This probably would be a very simple problem if I could use any theorem I wanted about poles and polars, but in the book they give a definition and they say the problem should be solved using only ...
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1answer
26 views

Geometry - Cyclic Quadrilaterals

Three points A,B,C lie on the circumference of the circle, with center as O. If angle(ACB) = 115 deg. Need to find angle (BOC)? Please post your approach?
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1answer
155 views

Can the $9$ point circle be generalized to $n$-gons of $n\gt3$?

All triangles have concyclic vertices and have a $9$ point circle which intersects the triangle's feet and the midpoints of its sides (as well as $3$ other significant points). Is this special for ...
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1answer
87 views

Geometry - prove, that the center of circumscribed circle of a triangle lays on line.

Inside the angle, which vertice is the point $M$, the randomly selected point $A$ is drawn. From this point the ball is released, which at first reflected from one side of the angle at point $B$, ...
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1answer
61 views

Plane-geometry problem with circles and tangents

I have a problem that even my smartest colleagues were able to solve. This is to get the radius of the smallest circle in the drawing below. Using a computer program, I managed to get that lightning ...
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7answers
312 views

area of figure in sector of intersecting circles

I need to find an area of blue part of figure APBC. I draw line segments between B and C, between C and A, and got equilateral triangle. I'm stuck here. Please help. Thanks. |AB| = a, P is midpoint ...
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1answer
61 views

Simple circle question

let AB be diameter of circle and AC be the chord. Let a tangent is drawn from C to meet AB produced at D.If BAC=30,Prove that BC= BD SOLUTION ACB= 90 ABC=60 CBD=120 After that I am confused
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1answer
137 views

How to calculate the range of angles at which a line will intersect a growing circle? Arc length?

I am working on some simulation software in which I have an entity (e) that is spiralling around a particular point (p). As e continues to move around p, the radius of the circle that it is following ...
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1answer
36 views

Is any property of orthocenter related in this question?

While practicing mathematics Olympiad questions , i got the below given question . Though the solution is given , I am not able to bypass certain steps ... Can anyone please explain me why angle KPA ...
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7answers
378 views

What kind of curve is made of half circles?

I have this curve. It's definitely no sine or cosine. It consists of half circles. How do you call it and how do you describe it mathematically?
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2answers
69 views

Equation of circle through three given points.

Yes, there are many methods to find the equation; the easiest being the process of solving the eqn. of circle putting the three points. But what I didn't understand is the another method which my book ...
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1answer
35 views

convex quadrilaterals and circles

Suppose you have an arbitrary convex quadrilateral call it $WXYZ$ and four circles with diameters $WX, XY, YZ, ZW$. How would you prove that the four circles would cover the whole quadrilateral ...
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2answers
295 views

Center of a circle from two chords.

If two chords of a circle intersect and are $\perp$ to each other, is it possible to find the distance from the intersection point of the chords to the center? I was trying to use the power of a ...
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2answers
361 views

Coordinates of the intersection of two tangents to a circle

Let $A = (x_A, y_A)$ and $B = (x_B, y_B)$. Let $\gamma$ be a circumference of radius $r$, centered in $(0, 0)$; $A$ and $B$ lie outside of $\gamma$, and on the same side of some line $L$ through the ...
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1answer
260 views

Place three circles such that they uniquely intersect at each point in the plane

Is it possible to place three circle centers in a plane such that there is a single unique three-way intersection between the three circles for any given set of circle radii? For example, see the ...
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2answers
49 views

How far to move a circle along a ray so that it intersects with another circle only once?

Given two 2d circles that have intersected at two points, how do I find the distance along a ray that passes through the center of one of the circles so that when that circle is translated along that ...
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1answer
39 views

Finding functions in Inscribed Triangle

If we have a circle of radius $R$ around center $O$ and its inscribed triangle $XYZ$ that is acute as well as scalene. $XY$ is the longest side. $XA,YB, ZC$ are the altitudes of the triangle $XYZ$. ...
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1answer
98 views

Equations for different quadrants of a circle

In the circle $x^2$ + $y^2$ = $a^2$, what's the general equation for the arcs in each of the quadrants?
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1answer
350 views

Distance between center of side of regular polygon inscribed in a circle, and the perimeter of that circle?

Point A : The center of a side of a polygon inscribed in a circle Point B : The point on the perimeter of that circle that is opposite Point A I want to calculate the distance between Point A & ...
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2answers
534 views

circular reasoning in proving $\frac{\sin x}x\to1,x\to0$

The classic proof for $\frac{\sin x}x\to1,x\to0$ is using a squeezing theorem based on arguments about areas of circles. But as far as I know, all deduction of formula of circles' area is based on ...
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1answer
50 views

Graphing Circles, Ellipses, Parabolas, and Hyperbolas

I need help plotting a curve on a graph where the distance from focus1 is always the same ratio to the distance from focus2. For instance, lets assume focus1 is -5 along the x axis, and focus2 is +5 ...
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1answer
274 views

Calculate distance in x,y from center based on distance and degrees.

I'm terribly sorry if this question is written like a 5-year old.. But that's the level I'm on in terms of math and coordinate calculations. (Just realized I don't even know what to tag this question ...
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1answer
147 views

Finding circle with two points on it and a tangent from one of the points

Two points P1(x1,y1) and P2(x2,y2) are known. In addition, a line slope passing through P1 is known. The aim is to construct a circle (or circular arc) that it passes through both P1 and P2 and it is ...
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1answer
96 views

Differentiation of a circle

As a discus thrower is spinning counterclockwise to throw a discus, the discus travels along the path given by the circle $x^2+y^2=4$. If the discus is released at the point $(\sqrt2,\sqrt2)$ and ...
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2answers
144 views

Beautiful triangle problem

Circle, inscribed in $ABC$, touches $BC, CA, AB$ in points $A', B', C'$. $AA' BB', CC'$ intersect at $G$. Circumcircle of $GA'B'$ crosses the second time lines $AC$ and $BC$ at $C_A$ and $C_B$. Points ...
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1answer
66 views

In every polygon circumscribed about a circle, there exist three sides that can form a triangle.

How can one show that in every polygon circumscribed about a circle, there exist three sides that can form a triangle? (This was posted by another user and then deleted while I was typing my answer.)
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Comparing The Rates at Which Squares and Circles Fill Large Similar Areas.

Consider these two search patterns. ${\square}$ A square moves in straight lines forming what you might call a "square-spiral" pattern as it covers a much larger square space. ${\bigcirc}$ A circle ...
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2answers
135 views

Number of ways to seat people around a circular table

I got (i) which is $9!$, but there are no answers for the second question. I stated that $$P(\text{none together})=1-P(\text{3 together})-P(\text{2 together})$$ and got the answer $7/12$. Is this the ...
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5answers
432 views

How can I find the radius of a circle from a chord and a section of the radius?

Draw a circle with center O. Line AD is a chord that is 8cm long. The arc above is smaller than the one below. B is the center of AD. Line CB is a line that is 2cm long. It meets AD at 90°. ...
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1answer
89 views

Computing overlapping circle positions, equidistant from each other.

Hello, I am a programmer and I wanted to develop an application that would have several overlapping circles in the same location, where each circle can be selectable. Is there a mathematical way of ...
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0answers
121 views

Find the minimum radius of the circle which is orthogonal to two given circles

Problem : Find the minimum radius of the circle which is orthogonal to both the circles $x^2+y^2-12x+35=0$ and $x^2+y^2+4x+3=0$ . Solution : Let the equations : $x^2+y^2-12x+35=0.....(i)$ and $x^2+...
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3answers
44 views

Cyclic quadrilaterals - finding the size of an angle

I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question ...
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3answers
46 views

Find the radii of the two circles which pass through the point $(16,2)$ and touch both axes

How can I find the radii of the two circles which pass through the point $(16,2)$ and touch both the axes? I've only ever seen demonstrations using three normal co-ordinates; or two normal co-...
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2answers
438 views

If the length of tangent drawn from an external point P to the circle of radius $r$ is $l$ , then prove that area…

Problem : If the length of tangent drawn from an external point P to the circle of radius $r$ is $l$ , then prove that area of triangle form by pair of tangent and its chord of contact is $\frac{rl^...
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1answer
272 views

Areas between intersecting chords

In the circle below let the two chords be called $C_1$ and $C_2$, and their intersection be some point that is not the center. The chord power theorem tell us that $a \cdot b = c \cdot d$. I am ...
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1answer
258 views

How to calculate point on circumference of circle given radius

I am trying to come up with a formula to calculate the y co-ordinate of the point on the circle in the attached picture (i.e. delta y) based on the circumference of the circle and the distance x. This ...
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56 views

Inverse with respect to a given circle

Determine the inverse with respect to a given circle $g:\mathbb{R}^{2} \to \mathbb{R}^{+}, g(x,y)=x^{2}+y^{2}$. I have looked around for non geometric derivations without finding any of value. ...
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2answers
451 views

Find the maximum perpendicular height between a chord and an arc.

I am doing a maths modelling project, and I am stuck on a part. I have a (arc length) and L (chord length), but I want to find H, the maximum perpendicular distance between them! Any help would be ...
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1answer
174 views

Show that the common tangents to circles $x^2+y^2+2x=0$ and $x^2+y^2-6x=0$ …

Problem : Show that the common tangents to circles $x^2+y^2+2x=0$ and $x^2+y^2-6x=0$ form an equilateral triangle. Solution : Let $C_1 : x^2+y^2+2x=0$ here centre of the circle is $(-1,0) $ and ...
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4answers
261 views

Equation of a line tangent to circumference

Discover the general equation of the tangent line to the circumference $x^2 + y^2 - 2x + 4y + 1 = 0$ by the point $(3,4)$. NO CALCULUS. by the circumference equation i discovered that $C(1, -2)$...
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1answer
73 views

intersection of 4 circles

Hi I'm doing some programming challenges for fun and I am trying to work out the maths required to solve this problem. It has been 10 years since I did any maths in anger like this so i'm a bit rusty....
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494 views

Infinite staircase to a circle

Suppose you start at $(0,0)$ on the unit disc and repeat the following procedure again and again: Face east and walk half-way to the circumference. Face north and walk half-way to the circumference. ...
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1answer
57 views

Circle Equation Surjectivity

Consider the circular function $g:\mathbb{R}^{2} \to \mathbb{R}^{+}$, $g(x,y)=x^{2}+y^{2}$. Show that it is surjective and continuous. Note This post has been amended in accordance with the ...
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3answers
896 views

How to determine family of circles passing through two given points?

The question asks to show that the equation of any circle passing through two given points takes a certain form. I have obtained the points as being $(2,1)$ and $(2,-1)$ but I'm not sure as to how to ...
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1answer
82 views

power of a point (circles) questions.

Lets say we have two circles call them $O_{1}$ and $O_{2}$. Let $a_{1}$ and $a_{2}$ be the arcs of the circles. Then when it comes to two circles, three cases arise. They intersect at two points, they ...
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174 views

Show that four vertices of a square cannot lie on four concentric circles, radii of which form an arithmetic sequence

My teacher said it's solved using proof through contradiction. I've considered cases of the centre of the circle, but I lose geometry big time so not sure how to do this.