Questions on the circle, a curve composed of points that are at a fixed distance from a fixed point.

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3answers
38 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:
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1answer
23 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 ...
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0answers
22 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 ...
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1answer
24 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 ...
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1answer
23 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 ...
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0answers
13 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 ...
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2answers
95 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 ...
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0answers
25 views

Help solve a geometry question involving circles and triangles [on hold]

To clarify, AB = 9, BP = 13 and PQ is tangent to circle. Find the length of PQ
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1answer
20 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 ...
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1answer
33 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 $d$ ...
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0answers
29 views

How do I apply the area of a circle to a college level of thinking?

I am writing a thesis on the area of a circle and I need more ideas on how the higher level college mathematics that deal with it.
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0answers
15 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 ...
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0answers
18 views

Find coordinates for point on circle

We got two points on circle and we know about center angle between two points.If we know coordinates of center $(x_1,y_1)$ and point $A=(x_2, y_2)$ and angle $\alpha$, how can we find the coordinates ...
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0answers
16 views

Can A circle be drawn without any reference point [closed]

Can a circle be drawn without any reference point. In other words by beginning only from one point can I draw any circle I wanted.
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2answers
44 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
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3answers
73 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
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1answer
19 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
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2answers
50 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!
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0answers
33 views

Circle geometry problem with overlapping circles

I want to find the length of the red line. The angle between radii is the same for both sectors and radii of both of the circles are known.
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1answer
25 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 ...
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1answer
35 views

Geometry/Trigonometry Homework Help - Circles

Help on this math problem: A regular Octadecagon (18 sides), each of whose sides are 14 inches, is inscribed in a circle. Find the radius of the circle, the size of each arc subtended by a side of ...
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1answer
15 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
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1answer
38 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 ...
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1answer
24 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 ...
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1answer
23 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.
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1answer
20 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 ...
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0answers
19 views

Chord of contact of pair of tangents

Prove that the chord of contact of the pair of tangents drawn from each point on the line $2x+y-4=0$, to the circle $x^2+y^2=1$ pass through a fixed point. Find the coordinates of this point.
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3answers
23 views

Equation of a Circle 245

Find the Equation of the circle which passes through the points $(1,-2)$ and $(4,-3)$ and which has its centre on the line equation $3x + 4y = 7$.
1
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1answer
36 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
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1answer
30 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
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2answers
49 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 ...
2
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2answers
53 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
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1answer
44 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 ...
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1answer
34 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
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1answer
34 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 $M$ ...
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1answer
37 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
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1answer
173 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
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1answer
33 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 ...
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3answers
87 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 ...
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2answers
30 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
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1answer
60 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. ...
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1answer
26 views

Determine the closest point along a circle's $(x_1, y_1)$ radius from any point $(x_2, y_2)$, inside or outside the radius of the circle.

I have a circle centered at point $(x_1, y_1)$ and another point at $(x_2, y_2)$. This point, $(x_2, y_2)$ may or may not be within the radius ($r$) of the circle. I wanted to create a line going from ...
0
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3answers
50 views

Calculating time for Roomba to complete a circle

I am not very good at mathematics and as such I hope I've come to the right place to ask this question. Currently, I am programming an iRobot Roomba to make a circle. All is well, except that I need ...
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2answers
27 views

How do I find the y coordinate of a point on a circle with the x coordinate and radius?

I have this situation (forgive my paint skills): I have the radius R, the x coordinate D, and the angle of the tangent a. How would I go about finding h, the y coordinate of that point? Thanks!
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0answers
26 views

How to prove that PH is containing midpoint of side MN from this circle and triangle problem?

Given: triangle ABC is acute triangle. M and N are midpoints of AB and BC respectively, while BH is altitude of triangle ABC. Circles AHN and CHM meet at point P. (P is not same with H) How to ...
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0answers
26 views

How to prove that P, F, and E are collinear from this following parallelogram problem?

Inside parallelogram $ABCD$ with $\angle A=90^\circ$, a circle with diameter $AC$ intersects $CB$ and $CD$ at $E$ and $F$ respectively. Tangent line of this circle at $A$ intersects $BD$ at point ...
4
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2answers
57 views

How to prove that the angle between two sides of that triangle is less than 60 degree?

The product of two sides of triangle is equal to 8*(R*r) where R is circumradius of this triangle, and r is inradius of this triangle. How to prove that the angle between two sides of that triangle ...
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0answers
19 views

circles & spirals

A man starts moving on the circumference of the circle of r=2, with const. speed of 4m/s. Another man starts moving from the centre of the circle at a const. speed of 4m/s such that he is always on ...
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3answers
280 views

What is the largest circle that fits in $\sin(x)?$

Imagine dropping a circle into the trough of $\sin(x)$. Would it reach the bottom or get wedged between two points on the curve? Depends on the size of the circle. So, what is the radius of the ...
1
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2answers
80 views

Three circles with two common points

Let $ABC$ be a triangle of any type and $A_1,B_1,C_1$ the feet of the heights. Denote $M,N,P$ the orthogonal projections of the point $A$ onto the lines $B_1C_1,C_1A_1$ and $A_1B_1$. The circes ...