# Tagged Questions

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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### find center of circle from one point,knowing radius

I have a problem that I have to solve. I need to find center of the circle containing the point $(x,y)$. The point is $x=2,y=3$ with radius $r=3$. I need to find the center of circle. Is there ...
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### Find circle for two points, one with given angle.

I have point A and B. I also have a vector v. How can I mathematically find a circle whose tangent at point C has the same angle as v where point C is the same as B and the circle also contains point ...
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### Why is the area of the circle $πr^2$? [duplicate]

I searched many times about the cause of the circle area formula but I did not know anything so ... Why is the area of the circle $\pi r^2$? Thanks for all here.
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### Counting regions in a disk that has been cut by lines

Let $n$ be a positive integer, and $n$ lines drawn in a ring such that each one of them intersects with all of them, but no more than two intersect at one point. prove that the lines cut the disk ...
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### Simple: Angle Between Two Angles of Circle

I want to be able to define a start and an end angle in a circle and then be able to come up with an algorithm that allows me to test if an angle is between the two angles (clockwise from start to ...
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### Convex hull of two circles

I have a small problem I've been trying to resolve for the last hours but with not succes. I have two circles in R^2, for each one I know it's center and radius = 1. I have a point somewhere in R^2. ...
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### Equation, Area and Circumference of A circle given equation of the tangent and center

I don't know how to solve for the Area and Circumference but I know how to solve for the equation but I just wanted to make sure... Any help and explanations would be appreciated :) Problem: A circle ...
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### find arclength given angle of circle in degrees and radius oif circle

I'm having a lot of difficulty with getting this to make sense and the answer in the book is just '8.4 in' Q " You want to make an 80 degree angle by marking an arc oin the perimeter of a 12-in. ...
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### Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
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### Prove that two segments are congruent in the arbelos

Background Info + Problem I teach HS Geometry to middle school age students. I generally like to try to solve problems instead of looking up the answer, but this week a student emailed me a problem ...
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### Find coordinates of point that intersects circle

I got a circle of 900 radius, knowing its center coordinates A(x1, y1) and got another point with also known coordinates B(x2, y2). I draw a line between point A and B. It intersects the circle in a ...
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### Circle in the plane of complex numbers

Let $K = \{z \in \mathbb{C}: |z−a|=r \}$ be a circle in $ℂ$. Show that, for the case that $|a|$ is not equal to r, the image of $K$ under the transformation $z$ $\to$ $\frac {1}{z}$ is a circle too. ...
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### The number of the circles which are tangent to two circles and to a line

Suppose that we have two distinct circles and a line on a plane and that the distance between the centers of the circles is bigger than the sum of their radiuses. Also, suppose that the two circles ...
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### Triangle, Circle Problem

What is the area $\triangle DEF$ ? I solved it using analityc geometry. I want to see if there is way to solve it using plane geometry. I did it: $x^2+y^2=400$ $(x+10)^2+y^2=100$ I found the ...
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### equation draws a circle in C

It be $a\in\Bbb C , b ∈\Bbb R$ and $|a|^2 > b$. Also, $a'$ is the conjugation of $a: a' = x - iy$ when $a = x + iy$ (and equally for $z$). It needs to be shown, that the solutions of the equation: ...
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### Two body problem (rotation around a fixed central point)

Is there a way which isn't physics related, but just using pure maths to find the solution to the following problem: If i have two lines of different lengths at t=0 overlapping each other. They are ...
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### A geometric problem where the result is obvious but the proof is hard…

So M and N are the midpoints of the bases AB and CD of the isosceles trapezoid ABCD. The bisectors of angles CAD and ACB intersect with MN at points P and Q respectively. K and L are on AC so that the ...
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### Calculate point P(x,y) in a circle given a radius and angle degree

I'm doing a program in Java to draw a PieChart based on given value as link below. data for piechart Given that the diameter, radius, angle degree, center point (150,150) and First Point A (150,0) ...
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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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### 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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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.) ...
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 ...
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 ...