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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Problem Involving Circle Geometry [closed]

A circle passes through the following points: $(0,0)$ $(1,3)$ $(3,0)$ and $(2,3)$ Find the centre and radius of the circle and explain why. Thanks for any help. So far I have drawn a graph, the ...
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1answer
19 views

Circleline points

How can I show that $\forall$ distinct $z_1,z_2,z_3,z_4 \in \mathbb{C}$, $\frac{(z_1-z_3)(z_2-z_4)}{(z_1-z_4)(z_2-z_3)} \in \mathbb{R} \iff$ the points lie on a circle? I don't really have a clue of ...
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1answer
26 views

X is any point on AB and the median AD of triangle ABC meets XC at Y.Prove that XY/YC = AX/XB

X is any point on AB and the median AD of triangle ABC meets XC at Y.Prove that XY/YC = AX/XB.
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2answers
24 views

Complex inversion map

How do I show that the map $f: \mathbb{C}\setminus \{0\} \to \mathbb{C}\setminus \{0\} $. $f(z): z \mapsto \frac{1}{z} $ maps circles to either a circle or a line?
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0answers
28 views

Prove the following represents a circle

I'm trying to prove the following represents a circle but I can't see how to reduce it down to the form $|z-z_0|=c$: Let $r \in \mathbb{R}, r \not= 0, c \in \mathbb{R}, k \in \mathbb{C} : |k|^2>cr$...
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1answer
15 views

determine the centre points of the circle

Given: Circle with centre $M (-5; 5)$ The equation is $(x+5)^2 + (y-5)^2 = 50$ Suppose this figure is translated $6$ units to the right and $3$ units down. What is the new centre of the circle? ...
2
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1answer
24 views

triangle park problem [closed]

We have a park that is triangle. We don't know the shape of the triangle and it can have any triangle shape and lengths. Where should we place a lamp to have light everywhere in the park? my english ...
3
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2answers
36 views

Equation of a tangent line for circles

When calculating a tangent to a circle, is the method the same as tangent to a curve? Problem: A circle has a radius of $2$ and is centered at the origin. Find the the equation of the tangent line to ...
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2answers
23 views

Geometric Sum of the circumference of the layers of a cake

The diameter of each successive layer of a wedding cake is 2/3 the previous layer. If the diameter of the first layer of a 5 layer cake is 15 inches, find the sum of the circumferences of all the ...
0
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1answer
22 views

How to plot concentric circles (or other patterns?) on a grid of pixels, ensuring every pixel is occupied

A hobbyist programmer asks... Let's say a "pixelMap" is an array of x,y coordinates in a square region at which to render each color that's read from a separate array (in order from start to finish) ...
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3answers
51 views

Finding End point of an Arc in Cartesian Coordinates while radius, arc length and one end of Arc is given?

The problem Picture I want to find the position of a robot using single tire model while rotating. I am assuming robot is moving along a circle. I know its radius, length or arc and starting point of ...
2
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3answers
65 views

How can I show that $AX=AY$?

In the diagram below, the two circles have equal radii. However after much bashing around with angles, I was not able to show that $AX=AY$. My only idea so far is to try to instead prove that $\...
2
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2answers
72 views

How to find the area of a semicircle inside of another semicircle?

I am stumped on how to solve this problem. I've tried to look up the problem, but to no avail. What I need to know is how can I find the area of a semicircle cut off by the curve of another semicircle?...
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1answer
33 views

4 circles one thread circling them [closed]

Can somebody tell me how to measure the length of a thread which is wrapped around 4 circles the radius of each is 1m. The four circles are touching but their ...
2
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2answers
80 views

How do you calculate the area of the intersection between a rectangle and a doughnut?

I'm dealing with an engineering problem, involving concentric pipes, with air flowing through the outer pipe (doughnut). I need a cross-beam to support the inner pipe, so I need to calculate how much ...
4
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6answers
227 views

How can never ending decimal numbers represent finite lengths? e.g. pi(π), $\sqrt{2}$

Recently, I was in a discussion with a colleague that, whether the πd really can represent the accurate perimeter of a circle or not. To clarify that doubt, I came ...
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1answer
27 views

How to find the intersection coordinate with circle and line equation?

http://i.stack.imgur.com/krUqK.png Example we have one line and one circle above, and its equation are: Circle: $(x-a)^2 + (y-b)^2 = r^2$ Line: $y = m(x-x_1) + y_1$ How do we find the ...
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2answers
56 views

Find the circumference of a circle, given a chord and the length of the rest of the circle [closed]

If you know the measure of a chord in a circle as well as the length of the circumference minus the arc can you find the circumference of the circle? I can make a mockup image if it would help!
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3answers
39 views

Is this an equation of a circle?

Wanted to know why the following equation doesn't represent a circle: $2x^2 + 2y^2 − 6x + 4y + 7 = 0$ I know that $(\frac{-a}{2})^2 + (\frac{-b}{2})^2 - c \geq 0$ And it is, but the exercise says ...
0
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4answers
71 views

Properties of Equilateral Triangles in Circles

If there is an equilateral triangle in a circle, would the midpoint of any of the 3 sides be half the radius? e.g if the radius was 6 and at the midpoint of the triangle (call it B) would center to ...
1
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1answer
55 views

What is the equation of circle with radius $\sqrt{2}$, tangent to the line $x+y=3$, and having its center on the line $y=4x$? [closed]

What is the equation of circle with radius $\sqrt{2}$, tangent to the line $x+y=3$, and having its center on the line $y=4x$? Can someone help me please?
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1answer
30 views

Circles and mid bisector

Let the point $M -$ bisector middle $AD$ acute triangle $ABC$. A circle $\omega_1$ with a diameter of $AC$ intersects the segment $BM$ at point $E$, and a circle $\omega_2$ with a diameter of $AB$ ...
0
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1answer
36 views

minimum radius of circle tangent to 3 sides of quad

I have a convex quadrilateral defined (in counterclockwise order) by the points $$p_0=(x_0,y_0)\\p_1=(x_1,y_1)\\p_2=(x_2,y_2)\\p_3=(x_3,y_3)$$ I want to found the minimum radius between all the radius ...
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1answer
130 views

Shortest distance between two circles

What is the shortest distance, in units, between the circles $(x - 9)^2 + (y - 5)^2 = 6.25$ and $(x + 6)^2 + (y + 3)^2 = 49$? Express your answer as a decimal to the nearest tenth. So I know that ...
0
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1answer
74 views

Value Of $\pi$ obtained using limits!

What i thought was simple, a circle can be formed by increasing the number of sides of regular polygon( like pentagons, hexagons, etc ) up to infinity by keeping the distance between the center and ...
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2answers
24 views

$r<a, (x+a)^2 +y^2=r^2, (x-a)^2 +y^2=r^2$ four tangent lines

Find the equation of the four tangent lines which are tangent to both circles, $(x+a)^2 +y^2=r^2, (x-a)^2 +y^2=r^2$ Do not give it in the form that involves trigonometric ratios. What are the four ...
0
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1answer
58 views

How to rotate a line segment around one of the end points?

I am given x1, y1, x2, y2 and θ. How can I find x3 and y3? By the way, there can be another line segment on the other side of AB (as if the line was rotated counter-clockwise). How to find that too?
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1answer
22 views

Calculating radius of circles which are a product of Tangent Intersections using a Regular Polygon

Introduction Lets have a regular polygon of $n$ sides inscribed in a circle of radius $H$, then construct tangents between the circle and each point of the polygon and draw new circle(s) trough the ...
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2answers
33 views

If you colored every point of a circle 1 of 2 colors, is there always 2 same-colored points of distance $R$ apart?

If every point on a circle of radius $R$ in $\mathbb{R}^{2}$ were colored one of two colors, is there necessarily two points that are of the same color and of distance $R$ apart? what about $>2$ ...
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1answer
38 views

Can cyclic quadrilateral be a parallelogram $?$

Question: a) Can cyclic quadrilateral be a parallelogram $?$ b) Can a parallelogram be cyclic $?$ Solution: a) Cyclic quadrilateral can be a rectangle or square. They are also parallelogram. So ...
43
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2answers
3k views

Are similar circles really a thing?

I'm a fifteen year old who is currently studying circle geometry (if that is the appropriate term) and our teacher stated that concentric circles are similar. I thought about this, and it doesn't make ...
0
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1answer
28 views

Center of Circle given Apothem and 2 points

I am given 2 end points of the chord $AB$ as well as the apothem, the distance from the center point of the circle to the chord. I can easily find the radius circle and midpoint of the chord I'm just ...
4
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2answers
89 views

Fit 2600 equally spaced points on concentric circles

My friend is working on an art project where she wants to draw 2600 dots on a circular table, symbolising the 2600 deaths of the conflict in east Ukraine. She approached me to solve this, but I've run ...
8
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3answers
115 views

Show that $O$ traces out a circle in the pencil defined by $A$ and $B$

Show that $O$ traces out a circle in the pencil defined by $A$ and $B$
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1answer
38 views

Finding the area of the region bounded by the incircle and the sides of the triangle?

click here for the image In an isoscles triangle, we can find the radius of the incircle by using the fact that the angle bisector of the third (unequal) angle is the perpendicular bisector of the ...
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2answers
97 views

If A, B, C, D are four points on a circle in order such that AB = CD, prove that AC = BD.

If A, B, C, D are four points on a circle in order such that AB = CD. How do you prove that AC = BD.
3
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0answers
49 views

Centroid and circumcenter — how close?

Suppose $R$ is some planar region, bounded by a curve. Let $C_1$ be the centroid of $R$, and let $C_2$ be the center of the "circumcircle" (the smallest circle enclosing $R$). Intuitively, it seems ...
6
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1answer
70 views

Calculating radius of circles which are a product of Circle Intersections using Polygons

Lets say you imagine a circle with the radius $R$ and you inscribe a regular polygon with $n$ sides in it, whose side we know will then be: $$a=2R*sin(\frac{180}{n})$$ Then you draw a set of circles ...
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4answers
43 views

How far apart are centers of a set of Johnson Circles if the centers are equidistant?

I'm finding it hard to find the answer to this problem, I suspect it is simple and I'm missing something. Assume there are three circles with equal radius. The circumference of the circles intersect ...
5
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3answers
64 views

Is $\sin(x)$ =$-\sin(180^o+x)$?

I figured out that $\sin(x)$ should equal $-\sin(180+x)$ like in this picture But when I type on Wolfram $$\sin(a\mathrm{deg})=-\sin(180+a \mathrm{deg})$$ it says it's false. Why? I've tested it ...
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1answer
53 views

Three circles intersect at one point.

If three circles intersect at one point then there's unique $x$ and $y$ coordinate values such that the following equations are satisfied: $$(x-x_i)^2 + (y-y_i)^2 = r_i^2$$ Where $i=1,2,3$ Taking ...
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0answers
19 views

circle segment height by given fill fraction

At work I was facing the problem of how to calculate the height of a water column inside an horizontal cylinder given the volume of the liquid. A plot of this function and a visual explanation can be ...
2
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2answers
46 views

Bézier curve approximation of a circular Arc

I would like to know how I can get the coordinates of four control points of a Bézier curve that represents the best approximation of a circular arc, knowing the coordinates of three points of the ...
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1answer
37 views

length of a tangent

The two tangents to a circle are represented by $2x^2-3xy+y^2=0$ . A circle of radius=3 is in first quadrant . "A" is a point of tangency where one of these lines meet.What is length OA where $O$ is ...
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1answer
24 views

Formula for cycloid?

Is there a formula for cycloid? My approximation is $((2\times(x\div(\pi\div2)))-(x\div(\pi\div2))^2)^.626$.
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0answers
38 views

Find center and radius of circle with n# of equally spaced points

Say there is a point P, with coordinates $(x_1,y_1)$, and there is a circle that passes through this point, and the origin. There are n# of equally spaced points that lie on the circle leading from ...
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1answer
47 views

Finding the area of a part of two internally touching circles [duplicate]

Two circles touch each other internally at point A as shown in the figure: (http://imgur.com/hmzgMCT) O is the centre of bigger circle. If CB = 9 cm and DE = 5 cm. Find the area of the crescent ...
3
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4answers
84 views

Semicircular paper and creasing of a chord

A semicircular piece of paper with radius $2$ $cm$ is folded along a chord so that the arc is tangent to the diameter.If the contact point of the arc divides the diameter in the ratio $3:1$,determine ...
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1answer
54 views

How to adapt “System of Circles” method to 3D for finding a sphere given 4 points?

I want to analyze (computational complexity & running time) of different approaches to determining a sphere in 3D given 4 points on its surface. To start I have been searching for different ...
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1answer
64 views

Find the coordinates of the points where the two circles intersect. [duplicate]

The two circles are: 1) $$(x-2)^2 + (y+1)^2 = 25$$ 2) $$(y-2)^2 + (x+1)^2 = 25$$