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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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 ...
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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. ...
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1answer
155 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 ...
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3answers
160 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
210 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
75 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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3answers
395 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
126 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
179 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
414 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
79 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
84 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 ...
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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 ...
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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
70 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
62 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
138 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
504 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
121 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
326 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 ...
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1answer
621 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?
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1answer
167 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.
2
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1answer
92 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
127 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
117 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
849 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
92 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
56 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
471 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
337 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
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1answer
609 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 ...
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4answers
103 views

Name of the Angle of a unit circle's radial line from the positive X-axis

For the unit circle on a X-Y plane, is there a name for the Angle a radial line makes with the positive X-axis? The closest name that I can get from Wikipedia is a 'Central Angle' ( ...
2
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1answer
92 views

Circles partitioning the plane [duplicate]

What is the equation for the maximum number of regions into which N circles can partition a plane? Is there a name for this equation? A single circle partitions the plane into two regions, inside ...
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1answer
77 views

How to find the coordination of a tangent point on a circle?

I have a circle with the radius R, and coordinates of point A outside of the circle, and the coordinates of the center of the circle. I need to find the exact touching point of the tangent from point ...
2
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2answers
777 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
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1answer
80 views

Does an infinite collection of circles accumulates at a circle?

There is an infinite collection of closed circles in the plane, all within a finite bounding square. Does it contain an infinite sequence of circles that converge to a circle? Assume that a point is ...
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1answer
581 views

How to find the “as the crow flies” distance between two points that lie on a circle?

So I heard what I thought was a clever answer to "How do you make 2+2=5?".. On a 9-mile long circular track, drive two miles, then two more miles. You will be 5 miles from your start position. ...
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3answers
164 views

How to check whether a line exists inside a circle or not?

I have a line equation in the form of ax + by +c = 0. And I have a circle with radius r. I want to know whether the line exists inside the circle or not??
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3answers
374 views

equation of tangent to a circle with zero gradient

Find the equation of the tangent to the circle $$(x-3)^2 + (y-2)^2 = 1$$ at the point $(4,2)$. I cannot show the working of the tangent equation as gradient/slope = 0. So how can I find the gradient ...
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1answer
163 views

hyperbolic geometry (and circle ) construction problem

Was thinking about hyperbolic geometry, the Poincare Disk Model and Sweikarts constant and combined them all in a construction puzzle that I was unable to solve. My construction puzzle: Given: A ...
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0answers
1k views

Rounding Corners: How to calculate Fillet radius?

How do I find the maximum rounding I can apply to either corner for any amount of rounding on the other corner? The all circles are perfect circles, but I can't figure out the max size of the ...
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1answer
78 views

Geometrically prove that for a point on a diameter…

Geometrically prove that for a point on a diameter between the center point and the perimeter of a circle, the distance between this non-center point is the shortest distance to the perimeter. So $A$ ...
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2answers
496 views

Paramtrizing a counterclockwise circle vs. a clockwise one

Does it make a different when you parametrize a counterclockwise full circle and a clockwise circle in the complex plane? For example, I am looking at computing an integral $\int_\gamma ...
2
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2answers
469 views

Formula for semi circle with diameter up?

So I know the formula for a semi circle is $$y = \sqrt{r^2 - x^2}$$ However, what if I wanted to find the equation for a semi circle who's diameter is at the top of the graph? Would this be the ...
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1answer
652 views

Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
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3answers
3k views

Angle between tangents and angle subtended by radii are supplementary

Using the result that the length of the tangents draw from an external point to a circle are equal, prove that the angle between the two tangents drawn from an external point to a circle is ...
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1answer
118 views

Find the length of the common chord $PQ$

Two circles with centres $O$ and $O \ '$ of radii $3$ cm and $4$ cm, respectively intersect at two points $P$ and $Q$ such that $OP$ and $O \ 'P$ are two tangents to the two circles. Find the length ...
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1answer
338 views

Linear distance is proportional to angular distance, why?

Im my Fourier series book, the following is stated: We may specify the position of a point on the circle by its angular coordinate $\theta$, measured from some fixed base point. Since linear distance ...
3
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1answer
1k views

Two circles touch internally

Hello I've bean practicing for competition in math and can't seem to solve this problem,tried drawing chords,tangents,finding equal triangles,but couldn't seem to solve it.Any help would be ...