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.

learn more… | top users | synonyms

0
votes
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: ...
0
votes
1answer
293 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: ...
1
vote
0answers
332 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 ...
0
votes
3answers
36 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?
2
votes
1answer
108 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 ...
4
votes
1answer
322 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 ...
0
votes
1answer
208 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 ...
2
votes
2answers
443 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 ...
-1
votes
2answers
480 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.
1
vote
2answers
7k views

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 ...
1
vote
1answer
89 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 ...
4
votes
1answer
179 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?
1
vote
2answers
40 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 ...
2
votes
3answers
163 views

Equation with k describing a circle

My equation is the following, and I would like to find which $k$ can make it a circle. $$x^2+y^2+4x-6y+k=0$$ My naive approach is to have $k$ to be $-4x+6y+c$ where c is any number, so that I can ...
1
vote
1answer
67 views

2 pi term in sinusoidal signal

My intuition is that the $2\pi$ term in the sinusoidal signal equation: $$x(t) = \sin(2\pi\,f\,t)$$ Is indicative of the fact that this signal can be described as movement around a circle, is that ...
0
votes
1answer
330 views

How do I calculate the height of a cross section of a circle?

I'm working on an LED lighting project and have discovered that it involves a little math... I'm mounting LEDs to plexiglass facing away from the surface I want lighted. I'm looking at cutting a ...
3
votes
1answer
532 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
1
vote
0answers
230 views

angles subtending arcs at the circumference and centre

$A$ and $B$ are two points on the circumference of a circle center $O$. $C$ is a point on the major arc $AB$. Draw the lines $AC$, $BC$, $AO$, $BO$, and $CO$, extending the last line to a point $D$ ...
0
votes
2answers
35 views

circle measure - i don't know what method im supposed to apply

C(5,3) is the centre of a circle of radius 5 units. Show that this circle cuts the x-axis at A(1,0) and B(9,0) im guessing simply drawing it with a compass is not what im being asked here. i dont ...
0
votes
2answers
82 views

Solving angles within a cyclic quadrilateral

Please could you help with solving angles x and y as well as writing how you solved them.
0
votes
1answer
28 views

Finding the equation of a tangent of a circle at a point

The line with equation y=mx is tangent to the circle with centre (-8,0) and radius 4 at the point P(x,y) Show that $m=\pm\frac{\sqrt{3}}{3}$ and hence find the coordinates of P
3
votes
4answers
1k views

Integration for finding the Arc Length of Circle $x^2+y^2=a^2$

Question: Find the arc length of the circle given by $x^2+y^2=a^2$. $Ans = 2\pi a$ How to obtain the ans? I have no ideas after doing the following thing. Thank you for your ...
0
votes
2answers
319 views

Proving the inscribed angle theorem

I need to prove that a circle's inscribed angle is 1/2 of the arc it intercepts. I am given that one of the chords making up the angle is the diameter. I have an entire project to do based off of this ...
3
votes
1answer
197 views

How to create a two circle Venn diagram with 3 equal sections?

I had a student ask if I could draw a Venn diagram in which each region was of equal area. I have played around with this a little but have not landed on an answer I'm satisfied with. I was able ...
6
votes
2answers
128 views

3 circles and 3 squares all inscirbed into a right angled triangle problem

This is quite a tricky question for me, but this is how far I got: My drawing may not be precise, but I do know the points of tangency. I am a little stuck now, and I would appreciate it if someone ...
3
votes
0answers
145 views

unit circle trigonometry where angles is greater than 90

how is possible to have sin of angle greater than 90. if sin is ratio of opposite side and hypotenuse in right angle triangle then triangle with one of the angle greater than 90 can not be right angle ...
2
votes
2answers
153 views

Prove that this segment bisects another

The circle touches the trapezoid $GFEC$ at the points $C$, $D$ and $E$. The point $A$ is the center of the circle. The rest of the information can be seen in the diagrams below. What we have to ...
1
vote
3answers
384 views

$1$ big circle formed by$20$ smaller circles

Hello i need to make a circle out of 20 smaller ones. The smaller circles radius is r=9.3cm heres what i wanna do:
1
vote
1answer
103 views

Mapping a distorted ellipse onto a circle

I have a circular label pasted on a cylindrical object. In the image, this circle looks like a asymmetrical ellipse. I know the radius of the cylinder and that of the label. What mapping do I need to ...
0
votes
1answer
59 views

How many ways can we place two types of balls on a circle?

There are $a$ red balls and $b$ blue balls, and I have to place all of these balls on circumference of a circle. The balls with the same color are indistinguishable. I thought the answer would be ...
1
vote
1answer
748 views

Area inside cardiod $r=2-2 cos (θ) $ and circle $r=-6cosθ$

I found the points of intersection $(3,2π/3)$ and $(3, 4π/3)$ but now I'm stuck and don't know how to continue. I don't know how to choose the range of numbers to integrate. The answer is 5π if it ...
0
votes
1answer
124 views

Circles (Locus of a Point)

Problem: Find the locus of a point the sum of the squares of whose distances from $(2,3)$ and $(-1,-2)$ is $34$. Solution: Source: Schaum's 3000 Solved Problems in Calculus I read that locus ...
0
votes
0answers
70 views

draw a circle using beizer curve and co-ordinate of control points

I want to draw a circle of radius R centered at the origin using Bezier Curve Segments. I have to draw the circle using four Bezier Curve segments - one for each quadrant as shown in the following ...
5
votes
2answers
322 views

Relationship between circles touching incircle

I am trying to derive a relation between radius of those outer circles and radius of the incircle. Those outer circles are tangent to the incircle and respective sides. I have tried and failed ...
2
votes
1answer
68 views

Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval $(0,1)$

Be $S^1$ the unit circle in the plane, that is, $S^1= \lbrace (x,y) : x^2+y^2=1 \rbrace$ with the subspace topology. Show that $S^1 - \lbrace (1,0)\rbrace$ is homeomorphic to the open interval ...
2
votes
1answer
53 views

Intersection of an $n-$sphere and a plane (when non-empty and not a point)

Let the n-sphere of radius $r$ centered at $(0,0,...,0,y)\in\mathbb{R}^{n+1}$ be defined by $$ \mathcal{S} \iff {x_1}^2 + {x_2}^2 + ... + {x_n}^2 + (x_{n+1}-y)^2 = r^2 $$ and consider the function $d$ ...
1
vote
1answer
303 views

Find coordinates for points on circle given R, 2 Points, and angle or 2 points and center?

I would like to find coordinates for points on a circle given: Radius of circle Coordinates of 2 points on the circle Angle of point 1, center, and point 2. Ultimately, I would like to write a ...
0
votes
2answers
226 views

Is it possible to generate a circle with a Bezier curve?

I am designing an algorithm that generates shapes of bezier curves. Each output are control points for a single curve. In some cases, it should return a circle. Which control points does the ...
2
votes
3answers
101 views

Finding circumcentre

Tangents are draw from $P(2,3)$ to $x^2+y^2=4$ meeting at $Q,R$ on circle. Parallelogram $PQSR$ is completed. Find the circumcentre of triangle $QSR$. My attempt: Clearly, the parallelogram is a ...
0
votes
1answer
31 views

Simple algebraic question mixed up

I know it is very simple but do not know why I am mixed up in it $(.5)(r^2)\cfrac{20-2r}r$ how is this equal to $10r-r^2$ Sorry if it is too easy, thanks for the help.
2
votes
2answers
68 views

Find $\int_\Gamma\frac{2z+j}{z^3(z^2+1)}\mathrm{d}z$ where $Γ:|z-1-i| = 2$

pls, some ideas for integral solution (residue theory)? $$\int_\Gamma\dfrac{2z+j}{z^3(z^2+1)}\mathrm{d}z$$ Where $Γ:|z-1-i| = 2$ is positively oriented circle. Thx, for help!
1
vote
1answer
26 views

Is there another way to solve the value field of a parameter of an line.

Assume $P$ is a point in line $x+y=m$, where $m \in \Bbb{R}$. There are two points $A,B$ in circle $$x^2+y^2 = 10$$ such that $PA$ and $PB$ are tangent lines of the above circle. If line: $x+y=m$ has ...
1
vote
1answer
33 views

Make a point orbit another point, given time and a normal.

I am working in 3D space. I am trying to make a solar system model. known variables: center of orbit, C (x,y,z) normal, perpendicular to the orbit, N (x,y,z) radius of orbit, R time, position ...
3
votes
1answer
192 views

Locate a point a given distance from another point on an ellipse

Similar to Point on circumference a given distance from another point, but for an ellipse. Unfortunately, the difference is non-trivial. I have an ellipse and a point (C) that is somewhere on the ...
0
votes
1answer
60 views

fixed length random chord outside of circle.

consider a uniform distribution on a unit circle, I construct a cord by the following steps: pick one endpoint A within the unit circle uniformly. points that are $0<d<1$ distance away from ...
1
vote
1answer
30 views

Computing distance in circle

It seems to me as pretty simple, but I just can't get hold of it: I am trying to compute fn(x, r). Thanks.
1
vote
1answer
41 views

Find the area of region.

A chord of length R divides a circular area of radius R into two regions. Find the sides of the rectangle with the largest area that can be inscribed in the smaller region with one side along the ...
2
votes
1answer
500 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...
0
votes
1answer
490 views

A circle is inscribed inside a sector of a circle. Given the radii of both , find the length of segment formed by joining the endpoints of the sector.

$AOB$ is a sector of a circle with center $ O$ and radius $OA = 10$. Circle with radius $3$ is inscribed in this sector such that it touches radius $OA$, radius $OB$ and arc $AB$. Find the length of ...
1
vote
2answers
130 views

Three sides of a $\triangle$ are known. If a circle with it's center on base of $\triangle$ touches the other two sides , find the radius of circle.

In $\triangle ABC$, $AB = 10, AC = 12$ and $BC = 18$. A circle is drawn such that its center is on side $ BC$ and it touches lines $AC$ and $AB$. Find the radius of the circle. By pythagoras ...