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 $\int_\Gamma\frac{2z+j}{z^3(z^2+1)}\mathrm{d}z$ 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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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 ...
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1answer
34 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 ...
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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 ...
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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 ...
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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.
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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 ...
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1answer
505 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 ...
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1answer
504 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 ...
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2answers
131 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 ...
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2answers
248 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, ...
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1answer
97 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
75 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 ...
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1answer
171 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
48 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?
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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 ...
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1answer
54 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
356 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
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2answers
123 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 ...
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1answer
92 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
146 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
144 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 ...
0
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2answers
189 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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2answers
74 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 ...
17
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3answers
383 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 ...
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2answers
123 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 ...
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1answer
173 views

How to find the circumcircle radius from this following regular hexagon?

Given a regular hexagon $ABCDEF$. We draw diagonals $AC$ and $CE$. Then, we choose two points in the hexagon's diagonals(AC and CE), call that $M$ and $N$, such that: $\frac{AM}{AC} =\frac{CN}{CE}$. ...
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1answer
364 views

Area of circle formed when sphere is sliced by a plane

First off, when a sphere is cut by a plane, is a circle always formed or does a ellipse get formed in some cases? If a circle is always formed, how do you prove it? Next, how would you find the area ...
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1answer
76 views

Cauchy's integral formula used on circle

If $\gamma$ is a piecewise, smooth, positively oriented simple closed curve in $D$, then Cauchy's formula states that $f(z)=1/2\pi i\int_\gamma {f(a)\over {a-z}}$. My textbook also stated that for ...
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1answer
83 views

Determine the radius of the circle knowing that…

I have such a problem: determine the radius of a circle in which you know that two chords of lengths $9$ and $17$ intersect in a point, and that the distance between the middle points of these chords ...
27
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4answers
2k views

Two circles inside a right angled triangle!

The other day I was playing with Ms Paint drawing circles here and there - I coincidentally drew a circle inside a right angled triangle which I already drew. Strangely A problem struck to my mind ...
2
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2answers
83 views

Why does the “T=0” method to calculate tangent work?

Given a random equation of a curve: $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. Suppose we need to find the tangent to this curve at any point $A(x_1, y_1)$. A method given to me by my professor was the ...
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0answers
68 views

Grid overlay on an annulus. Move n squares to create a sector that is closest to the area of the original.

I want to create an image in photoshop, and need to break an annulus, pictured below, into smaller segments. I can use other methods to find the solution, but I'm interested to see how mathematicians ...
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0answers
59 views

Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
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1answer
129 views

Crossing Circles

On a plane, you are only allowed to draw circles. After drawing 1 circle, can you ALWAYS draw another so that the new circle crosses all existing circles at 2 points? Why?
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1answer
444 views

Inner tangent between two circles formula

As a programmer I need to draw the inner tangents between two circles, but only the segments, not the whole line. But the internet is surprisingly hostile to lazy programmers who don't know their ...
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1answer
114 views

How to get points to draw chord(diameter) on circle

Please consider the figure below: I hope I am asking my Question in right forum.. I want to get set of paired points on circle using diameter. What I have is center point of circle and its ...
3
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1answer
298 views

Circle touching three circles

For some tasks to prove I need to know if there always exists a circle which is tangent to three given circles but contains none of the three given circles. It is ensured to have middle radius smaller ...
0
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1answer
507 views

If the arc length and chord length between two points in a circle are known , find radius of the circle? [duplicate]

If the arc length and chord length between two points (two points on a circle that constitute a minor arc ) in a circle are known , find radius of the circle?
3
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1answer
162 views

Length of median extended to the circumcircle

A triangle has side length $13,14,15$, and its circumcircle is constructed. The median is then drawn with its base having a length of $14$, and is extended to the circle. Find its length.
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1answer
86 views

Let C be a circle. Show that the only subset of C homeomorphic to a circle is C itself

I am trying to answer the question stated in the title. The hint in my book says to realize that for any z on the circle C{z} is still connected. I believe I can deal with case that shows that C{z} ...
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1answer
117 views

Tangent to the circle given a point it must pass through a point on another circle

I need to find the angle at origin caused by two lines (one is the radius of one circle, and the other is tangent to the other circle). Please see image below: The Point A on the green circle is ...
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2answers
92 views

Circle Area formula question

Take a peek at the following proof Everything makes sense but one thing: how did they determine that $\sqrt{\cos^2\theta}$ was positive and not negative? Thanks.
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1answer
699 views

Algebraic Proof that a Disk is Convex

After searching on Google for a while, I cannot seem to find an algebraic proof that a disk is a convex set. Intuitively, this seems obvious: if you take any two points $x, y$ in a disk, then the line ...
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1answer
87 views

Points of intersection of a line with two circles

I have the following representation: - line pass through the centers of the circles I have to find the coordinates of the points of intersection of the line with circles (4 points). From these 4 ...
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2answers
22 views

Get the trigonometric angle given a point in plane

Given a point in plane as (x,y) get the trigonometric angle for it (that being in range [0,360) or [180,-180)). Can someone give me a hint please ?
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1answer
55 views

Tangents to a circle

For this construction, how would you show that the perimeter of the triangle $CDF$ is equal to $2BC$? Please include steps and whatnot.
2
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1answer
455 views

Equation for concentric circles?

I want an equation for concentric circles. In following image I am trying to draw concentric circles in Java but as you can see these are messed up. This is because their (x,y) coordinates (i.e. ...
2
votes
1answer
258 views

Coordinates of sector of circle

I know the coordinates of one point on a circle, this point is part of a sector. I know the angle of the sector at the centre of radius, I know the radius and I know the arc length. How do I calculate ...
2
votes
1answer
543 views

Finding the points of a circle by using one set of coordinates and an angle

I know the image below isn't to scale and that the angle isn't quite at the centre point but can we just imagine it is picture perfect.... I know the coordiantes and point (x,y) lets say they are ...