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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1answer
126 views

Deflection formula doesn't work when angle is 0

I am trying to make objects bounce off of a circle in a realistic direction. The equation is $new = \theta - 2N * \theta N$ Where $\theta$ is the object angle in degrees, $new$ is the new object ...
6
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1answer
188 views

Prove that these 3 points are in a straight line

$\triangle ABC$ is equilateral with a circle $\omega$ inscribed in it. MN is a tangent of $\omega$ and it intersects $AC$ and $BC$ at points $M$ and $N$ respectively. $AM_1=MC$ and $BN_1=CN$. ...
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2answers
67 views

Calculate continous points on a circle circumference

Known details Circle radius r Origin (x,y) starting point in circumference say (u,v) I ...
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1answer
97 views

How large can a circle's radius be in an ellipse?

I have an ellipse centered on the origin parameterized by $a$ and $b$. Given its $x$ coordinate, how large can its radius be and still have the circle inside the ellipse?
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3answers
3k views

Number of Squares in a circle

I a math question, that I hope someone can help me with. I have 342 Squares sized at 11 x 11 cm and need to calculate how to pack them in a circle and find out how large the circle must be to pack ...
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2answers
571 views

Calculating circle in taxicab geometry

I struggle with the problem of calculating radius and center of a circle when being in taxicab geometry. I need the case for two and three points including degenerate cases (collinear in the three ...
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4answers
392 views

Check whether $n$ disks intersect

I struggle with the following problem: Given $N$ disks $D_i = (x_i, y_i,r_i)$, calculate whether they ALL intersect. $D_1 \cap D_2 \cap \dots \cap D_N = \emptyset $ ? I do not care about the ...
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1answer
60 views

Unit circle - how to prevent backward rotation

Let's assume we have a unit circle (0, 2$\pi$). Basically I have a point on this circle who is supposed to move only forward. This point is controlled by the user mouse and constantly calculate 25 ...
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2answers
750 views

radius of circle inscribed in rectangle

I have two circles inside a rectangle(4 * 6), where the diameter of one of both is the total length of a side of the rectangle, and the other circle diameter is part of the length of the another side. ...
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2answers
2k views

Derive formula for area of a circle from formula from area of rectangle

I need to explain how to derive the formula for the area of a circle from the formula for the area of a rectangle. The area of a rectangle is length(width) and the formula for the area of a circle is ...
3
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1answer
221 views

Prove that these 3 points are in a straight line.

A triangle ABC is inscribed in a circle $\omega$. $BB_1 $ bisects $\angle ABC$ (and so $M$ is the midpoint of the arc $AC$ ($B \notin AC$, where $AC$ is the arc)). $B_1K \perp BC$ ($K\in\omega$). ...
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1answer
73 views

Length of hypotenuse

Let a circle centered at $O$ have radius $OA=10$. Let OB be perpendicular on OA.Let G and E be points respectively on on OB and OA.Let F be a point on the circumference such that GFEO is a ...
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2answers
627 views

Find a circle orthogonal to two other circles

Given two circles $x^2+(y-4)^2=4^2$ and $(x-8)^2+(y+2)^2=2^2$ I need to find the circle that's orthogonal to both the above circles, and contains the point $P=(8,4).$ Is there an algebraic way ...
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1answer
3k views

Finding the equation of a circle from given points on it and line on which the centre lies.

What are some effective ways to find the equation of a circle when you are given points lying on the circle and the equation for the line on which the centre of the circle lies. Here is an example of ...
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1answer
435 views

Computing a matrix to convert an (x,y) point on an ellipse to a circle

I have an ellipse defined by its semi-major axis, inclination, and position angle. The ellipse is centered on the origin. I would like to solve for a matrix that converts this ellipse to a circle. ...
0
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1answer
67 views

Calculating the Apollonius Circle

This is a followup to a question I asked earlier. I have looked for an example on Google and StackExchange, but I have yet to see a clear example of the formula to determine the equation of an ...
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4answers
886 views

Area of intersection between 4 circles centered at the vertices of a square

The centers of four circles are at the vertices of a square of sidelength 100m. Each circle has the radius of 100m. Which is the area of their intersection?
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3answers
229 views

Prove that a circle has an infinite number of tangents

It seems obvious that a circle is comprised of the set of all points that are equidistant from one point, and that each point on the circumference of the circle represents a tangent. This seems to ...
3
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3answers
272 views

Infinite series of tangential circles?

I want to show that for all $n$ there is some collection of $n + 2$ circles such that two of the circles ($A$ and $B$) are tangential to each of the remaining $n$ circles (but not to each other) and ...
3
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0answers
28 views

How does this polar function behave?

I came across this question in my textbook for Nonlinear Optimisation and I don't know what to do: Consider the function: $$ f(x_1,x_2)=(r-1)^2-\frac{1}{2}(r-1)^2\cos \left( \frac{1}{r-1}-\phi ...
1
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1answer
78 views

Number of ways to form isosceles triangle by picking points on a circle

Given a circle with 24 evenly spaced points, how would you find the number of possible isosceles triangles (which includes equilateral) that can by drawn using the points? My attempt was to say that ...
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2answers
47 views

Pidgeonhole principle - I'd like an explanation for this answer

A friend of mine showed me how to solve this question: suppose there are 5 black dots drawn on a blue sphere. show that there is a closed hemisphere such that 4 of the black points are in it. his ...
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1answer
55 views

M fibers over the circle then construct a symplectic form

I'm trying to prove that if a 3-manifold $M$ fibers over the circle, then $M\times S^1$ admits a symplectic structure. I know that it is an standard result. Probably it is very easy, but I can't see ...
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1answer
140 views

Circle containing three points, maybe all collinear

We all know that a circle is exactly defined by three distinct non-collinear points. But I need a way to solve the following problem (all in 2D): Given three points, calculate a circle with all three ...
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0answers
171 views

Can you explain the solution of this geometric problem

A year ago IBM research posted an interesting geometrical problem: A gardener plants a tree on every integer lattice point, except the origin, inside a circle with a radius of $9801$. The trees ...
3
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1answer
763 views

Solving circle's radius only knowing angle & lengths of external triangle OR solving for sides of a triangle partial side lengths

Is this possible? Given that I know the length of Y and Z and the angle of X can I figure out the radius A? If I can't without more information, I can produce another set of data X Y Z at a ...
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10answers
2k views

How is the value of $\pi$ ( Pi ) actually calculated?

When I was a child I was taught $\pi$ (Circumference/Diameter) is an irrational number and can be approximated to $22/7$ but $= 3.(142857)(\ldots)$. But where does this value comes from? In ...
2
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2answers
271 views

Why is the circle of convergence for complex power series a circle (and not e.g. a square)?

Power-Series have an "circle of convergence". With real numbers this is an interval. Expanding this to complex numbers this becomes a circle. There are lots of book stating this, but I did not find ...
2
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2answers
296 views

Prove that if two circles touch one another, then these chords, drawn from the tangency point, are proportional.

Prove that if two circles touch one another, then chords of the internal circle, drawn from the tangency point, are proportional to the chords of the outer circle that you get when you extend the ...
2
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2answers
65 views

On congruent chords

Let $C_i=C(A_i,r_i)$ two secant circles intersecting each other at $R,S$, with $r_1\neq r_2$. Let $M$ be the median point of $A_1A_2$. Let $t\perp RM$ at $R$, intersecting the circles at $X,Y$. I'd ...
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1answer
35 views

probability calculation for position measurement being inside a circle

Consider a position measurement that is prone to a random error in any direction. This would mean that the position would be in a circle where the probability curve taken across the diameter would ...
0
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1answer
593 views

Intersection of a parametric curve and a circle

Given a curve defined by a parametric equation $x(t)$ and $y(t)$, how might one calculate the point of intersection with a circle? The derivatives $x'(t)$ and $y'(t)$ are also available if they prove ...
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3answers
402 views

Proofs without words of some well-known historical values of $\pi$?

Two of the earliest known documented approximations of the value of $\pi$ are $\pi_B=\frac{25}{8}=3.125$ and $\pi_E=\left(\frac{16}{9}\right)^2$, from Babylonian and Egyptian sources respectively. ...
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1answer
40 views

stuck on a Cartesian question

we have a circle $(x-1)^2+(y-2)^2=9$ Point $P=(5,2)$ lies outside the circle. Solve the equation of the line which passes through $P$ and intersects the circle at two points whose mutual distance is ...
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5answers
490 views

How do I find/predict the center of a circle while only seeing the outer edge?

Question What formula would allow me to predict the center of this circle? In addition, what attributes of this image must be detected in order to predict the center? I figured understanding the ...
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5answers
5k views

Finding the shortest distance between a point and a circle

The question is "Find the shortest distance from the origin of the graph of the circle $x^2-14x+y^2-18y+81=0$ ". I found the circle in the following form: $(x-7)^2+(y-9)^2=7^2$ Then I found the line ...
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0answers
126 views

(PA)^2 + (PB)^2 +(PC)^2 + (PD)^2 is equal to?

A circle is inscribed into the rhombus ABCD with one angle 60. The distance from the centre of the circle to the narest vertex is equal to 1. If P is any point of the circle ,then $$(PA)^2 + (PB)^2 ...
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5answers
1k views

Can we prove that circle has at most two colinear points?

Ok so I stumbled across a problem(I found a solution just to be clear) and it got me thinking.The problem is a classic,it was challenge to prove that line can intersect circle in at most 2 points. So ...
0
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1answer
88 views

Fixed points through a general circle.

The circle $C: x^2 + y^2 + kx + (1+k)y - (k+1)=0$ passes through two fixed points for every real number $k$. Find $(i)$ co-ordinates of these two points and $(ii)$ the minimum value of the radius.
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1answer
205 views

An Unexpected Circle…

I played around with $$z=\frac{-1+e^{it}}{\phantom{-}2+e^{it}}$$ and found that, when I draw the real against the imaginary of $z$, it pretty much looks like a circle. But neither ${\frak{R}} z ...
2
votes
1answer
78 views

Contract expression of circle segment area contingent on height

I want to determine a function for the area of the segment's height. I have made it this far, but I would like to contract the equation further - sadly, I do not know how to do this while still ...
6
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2answers
151 views

Regular pentagon and tangent lines

We consider a regular pentagon $A_1A_2A_3A_4A_5$ and $(C)$ is its inscribed circle. We then, taking as centres the points $Α_1$,$Α_2$,$Α_3$,$Α_4$,$Α_5$, draw the circles ...
2
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1answer
292 views

Optimization: A certain amount of wire to create a square and a circle, minimize area.

You have 4 feet of wire to create a square and a circle. How much wire should you spend on each shape to minimize the area. Also, why isn't the minimum area when you use all of the wire on the ...
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5answers
228 views

If we are given a circle and its equation and a point which lies on it..can we find the diametrical opposite point?

If we are given a circle and its equation and a point which lies on it.. Can we find the diametrical opposite point?
2
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1answer
93 views

Nine-point-circle, midpoint of triangle

ABC is the triangle and M, N are midpoints of AB and AC. Points W, X are on AB, Y, Z are on AC such that WM = MX, ZN = NY. Let T be the intersection of WY and XZ, prove that T lies on the nine point ...
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1answer
104 views

Intersecting great circles to find position

Is it possible to find the intersection of two great circles when knowing the following: A point $a$ on earth, A point $b$ on earth, and The bearings of $a$ and $b$ from an observer?
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1answer
263 views

How to identify if points are on the left or right side of a circle

Suppose I have a series of points that are on a 2D plane, and I know they can be fitted to some part of the circumference of a circle. How can I determine that the points lie on the left or right ...
0
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1answer
131 views

Geometry GRE question

This is a GRE quesrtion, and I could not find the length to save my life, please help! A circle with diameter PQ of length 10is internally tangent at P to a circle of radius 20. A sqare ABCD is ...
0
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1answer
87 views

How to find the n number of coordinates of circumference of circle?

Line AB has two coordinates A = (1,3) and B = (1,6). How to find 10 uniform coordinates of a circumference of circle whoose radius is AB. Edit I tried this link but didn't get it.
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1answer
62 views

Bouncing of a ball from circular boundary

Lets say a ball with xspeed: 14, yspeed: 16 hits the circular edge at xposition:626 yposition:382 like on the below picture : It needs to bounce properly, to get the right bounce and new ball ...