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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2
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1answer
66 views

Requiring a Geometrical proof

In the figure, ABCD is a square circumscribing a circle ($\pi_1$) whose center is E, the point of intersection of the diagonals AC and BD. With A as center, AB as radius, sector ABD is drawn cutting $\...
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2answers
67 views

Finding whether the quadrilateral is cyclic or not

Is a quadrilateral with sides lengths $3$, $3$, $4$, and $4$ cyclic? Progress I found that sides joining 3 and 4 are of equal length. then I found that other diagonal should also have same length ...
11
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1answer
281 views

Is a line just an infinitely large circle?

A line is infinite, right? Well, if $-\infty = \infty$, then a line is an infinitely large circle. (Does this have something to do with $1/0$?) It seems wrong, is it? Could I disprove it? How would ...
0
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2answers
56 views

Sine on a Circle

I'm walking a quarter mile circular walking track. The width of the track is 8 feet across. If I walk from one side of the track to the other, walking a sine wave that has a 20 foot period, how much ...
0
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1answer
17 views

Simple Angle from X and Y Axes Input

I am trying, given the position along the $X$ and $Y$ axes from a controller, where the positions range from $-1$ to $1$ ($1$ being up on the Y and right on the X) to convert this to the direction of ...
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4answers
233 views

Finding the equation of a circle given one point and radius

What is the equation of the circle which passes through the point $(0,2)$ with radius $4$ and whose center lies on the line $y = x$?
0
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1answer
238 views

What is the radius of a circle tangent to two lines with a known angle between them

Given angle, $\alpha$, and distance, $d$, what is the radius, $r$, and angle, $\theta$, in the image below in terms of the known quantities?
0
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1answer
119 views

Drawing lines from tangents from two circles on both sides.

I need to draw two red lines connecting the tangents from two circles on both sides. I need an algorithm that would get them based on any angle these circles are in relation to another. I need the ...
0
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1answer
25 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
3
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3answers
76 views

Find equation of a circle

Find equation of a circle passing through $(1, 1)$ and touching the circle $$ x^2 + y^2 + 4x - 6y - 3=0 $$ at the point $(2, 3)$. I am stuck as I cannot find more than $2$ equations for $3$ unknowns. ...
1
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0answers
128 views

How to calculate the height of a segment based on radius and area

I'd like to calculate the height of a segment based on the area. I have the radius of the circle, the area of the segment and need to calculate the height of the segment. I found the following ...
0
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1answer
54 views

How to find circumference origin position?

I need to find origin of circumference which is defined by two points and vertex angle of isosceles triangle: I've got radius of triangle by ...
0
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2answers
57 views

Surface are of a lightbulb

I have this picture: How could I calculate the area of a "thing" in red square? It is a circle.
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1answer
69 views

Geometry: how to get the radius of a circle with just a chord of the circle

Answer: Able to find area with statement 1) The length of the segment AB is 10 Above are two statements asking whether I can solve for the shaded areas given the information they have provided. For ...
3
votes
0answers
80 views

Problem about cyclic quadrilaterals

In cyclic quadrilateral ABCD, let E, F, G, H be the orthocenters of triangles BCD, CDA, DAB, ABC, respectively. Prove that EFGH is cyclic. Progress So far, found that if E is orthocenter of BCD ...
0
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3answers
41 views

Express angular position of the Earth as a function of time

Say I have for example the Earth orbiting the Sun (in circular orbit) and I want to express angular position (in radians) as a function of time. Would I be correct in thinking that $2\pi/t$ does the ...
0
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1answer
31 views

Find a point on a cercle in an orthonormed system given an angle.

In this inverted orthonormed system, I need to find a formula that gives the x and y coordinates of a point on a circle in function of an angle A that have its top on the center of the circle. I know ...
0
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2answers
2k views

Finding Reference Angles in Precalculus?

I'm reviewing for an exam, and having some trouble with reference angles depending on the quadrant they lie in. For example, my book shows the following: I get the part about subtracting 12pi/6, ...
0
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2answers
2k views

To find two sides of a triangle when it is circumscribed a circle

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively. Find the ...
0
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1answer
25 views

Orbital Motion overlap

What's a possible way of finding time t for an overlap of three objects going around a circular orbit around a common fixed center. So like the solar system in 2D, How can I find the time for when the ...
0
votes
1answer
53 views

Calculating the length of an arc

I am working on some simulation software, in which I have an entity that is spiralling around a particular point. As the entity starts spiralling around the point, and the radius of the spiral ...
1
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0answers
28 views

Circles intersecting at A and B [duplicate]

Question: Two given circles intersect at A and B. A straight line through B meets the circles again at C and D. Prove that CD is greatest when it is parallel to the line joining the centres My ...
0
votes
1answer
87 views

overlap between orbitting planets

If two objects are orbiting around a common center point with different velocities and at different radius. The point in time in which they are overlapping can be found out using their angular ...
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2answers
2k views

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 ...
0
votes
1answer
57 views

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 ...
17
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6answers
847 views

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.
1
vote
1answer
68 views

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 $n^2+...
1
vote
1answer
283 views

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 end)...
0
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0answers
38 views

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. ...
0
votes
1answer
90 views

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 ...
0
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1answer
601 views

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. ...
0
votes
1answer
628 views

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 ...
3
votes
1answer
252 views

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 ...
2
votes
3answers
99 views

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 ...
1
vote
1answer
55 views

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. ...
10
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1answer
415 views

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 ...
3
votes
1answer
86 views

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 ...
1
vote
1answer
49 views

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: ...
0
votes
1answer
90 views

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 ...
2
votes
2answers
126 views

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 ...
0
votes
1answer
859 views

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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vote
2answers
608 views

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 ...
0
votes
1answer
93 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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vote
0answers
77 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 ...
0
votes
2answers
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 ...
2
votes
0answers
95 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 ...
0
votes
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?
8
votes
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 ...
1
vote
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 $B$, ...
1
vote
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 ...