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

1
vote
1answer
95 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
195 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
42 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
70 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
388 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
571 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
242 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
116 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
2k 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
390 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
222 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
133 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
157 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
156 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
440 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
113 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
60 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
1k 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
143 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
85 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
358 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
81 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
54 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
350 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
270 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
104 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
32 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
70 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
37 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
209 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
61 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
31 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
557 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
638 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
144 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 ...
3
votes
2answers
269 views

Surface Area of a Sphere

I'm having trouble with finding the surface area of a sphere, without using any calculus. What I thought, was that the surface area of a sphere is fundamentally an infinite number of rings, ...
1
vote
1answer
100 views

Identify the locus.

Let $A,B,C$ lie on a straight line. $B$ is lying between $A$ and $C$. Consider all circles passing through $B$ and $C$. The point of contact of the tangents from $A$ to these circles lies on ..... We ...
0
votes
1answer
80 views

Finding the release angle for projectile

Hello. I would like to create an game application for android platform that is similar like projectiles. I called it snowball machine. As you know regular projectiles has to hit the ...
2
votes
1answer
186 views

Inside a sector of a big circle , there are two touching circles. Find the radius of one of them.

Consider sector of a circle $OAB$. Circle with center $ M $ touches $OA$ at $P$, $OB$ a $Q$ and arc $AB$ at $N$. Circle with center at $L$ touches $OA$ at $C$, $OB$ at $D$ and circle with center $M$ ...
1
vote
1answer
50 views

Condition for intersection of chords inside a circle?

What is the condition for intersection of 2 chords inside a circle? Given n number of chords how to find the number of pairs of interecting chords?
2
votes
1answer
187 views

Finding a curve which satisfies a special condition about angle

We can see that the angle of $$\frac{x^2}{a^2}+\frac{y^2}{1-a^2}=1\ \ \ (0\lt a\lt 1)$$ from every point on $$C : x^2+y^2=1$$ is $\pi/2$. $\hspace1in$ Then, here is my question. Question : If ...
1
vote
1answer
57 views

If an ellipse has two radiuses, is there something like it, but with three or more radiuses?

If we say that a circle has one radius, and an ellipse has two, can I define figures that have three, four, or more radiuses? Also, how can I get that "radius"? In an ellipse that is 10 at its ...
0
votes
3answers
405 views

A circle is inscribed in sector of another bigger circle.Given A(circle) find the A(triangle formed by the center and the endpoints of the sector).

Consider sector of circle $MAB$. $∠AMB = 120◦$. A circle $S$ touches side $AM$, side $MB$ and arc $AB$ as shown in the figure. Area of circle $S$ is $75π/(7 + 4√3)$ . Find $4√3$ times the area of ...
0
votes
2answers
142 views

Geometry problem with 2 circles and a triangle

I tried to solve this problem: But I did not know how to do it so I looked at the answers and I saw E looked convincing because it is the only one that has square powers and D (from the diagram) is ...
1
vote
1answer
98 views

Simple Circle Problem

An elegant circle problem. It goes by many names. This is my version. Dog 1 is tied to a post by a leash 1 unit long. He shares half of his land with Dog 2 tied to a post 1 unit away from his own. ...