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

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0
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7answers
59 views

Is there any way to arrive at $\pi$ without mentioning the circle's radius or diameter? [on hold]

Given a circle of arbitrary size, is there any way to arrive at $\pi$ or $\tau$ (if you will) without any reference to the circle's radius or diameter?
0
votes
1answer
55 views

Topological entropy of circle homeomorphism is zero. True or false?

may I know if it is true that $\ f: S^1 \to S^1$ a homeomorphism, then $h_{top}(f) = 0$, where $h_{top}$ stands for topological entropy. I believe this statement is true, but I cannot prove it.
0
votes
1answer
40 views

How to calculate a, b, center of a ellipse with given bonding box of an arc [closed]

How to calculate the ellipse a, b, center, if only the bounding box of an arc, a start point and end point given. For example: (the angles are right = 0°, left=180°, top: minus, bottom:plus) Ellipse: ...
0
votes
1answer
3k views

Calculate using cross-section of tunnel [closed]

The figure shows the cross section of a railway tunnel. The radius of the tunnel is 3.5m, i.e $OA = 3.5\mathrm{m}$. $\angle AOB=90^\circ$. Calculate the height of the tunnel; the perimeter of its ...
1
vote
1answer
44 views

Show that a polar equation describes a circle

I want to prove that this polar equation: $$r^2 + 2r(\cos(\theta) - 3\sin(\theta)) = 4$$ describes a circle. I tried converting the equation into a cartesian equation and got $$r^2 + 2x - 6y = 4$$ ...
5
votes
4answers
154 views

Let $ABC$ be an acute angled scalene triangle.

Let $ABC$ be an acute angled scalene triangle. Let $P$ be a point on the extension of $AB$ past $B$, and $Q$ a point on the extension of $AC$ past $C$ such that $BPQC$ is a cyclic quadrilateral. Let ...
0
votes
1answer
25 views

Find the location of the center and the radius of the following circle: [on hold]

Find the location of the center and the radius of the following circle: $$ \left| \ \frac{z-1}{z+1} \ \right| \ = \ 3 \ \ . $$ $ \ z \ $ is a complex number. Thanks in advance!
4
votes
3answers
7k views

Calculating the coordinates of a point on a circles circumference from the radius, an origin and the arc between the points

We have a circle with the known radius $r$ and the circumference $2\pi r$, and we know a point $P_1$ somewhere on it's circumference. Now, we want to get the coordinates $[x_{P_2},y_{P_2}]$ of the ...
2
votes
2answers
116 views

How do I calculate a point on each of three circles that have specific distance to each other?

I am trying to write code for a computer simulator. I need to simulate a complex mechanism where each link has a known length and the ends of the links are connected to a triangle. I would like help ...
3
votes
1answer
5k views

Three tangent circles inside a larger circle

Suppose you're given a circle with center $O$, I'm curious, how can one construct with ruler and compass three circles inside the larger circle such that each is tangent to the larger circle as well ...
2
votes
3answers
56 views

$N$ circles on a circle

Perhaps a rather elementary question, but I simply couldn't figure out the calculations on this one. Say one takes a circle centered at the origin with radius $R$. He or she then proceeds to place $N$ ...
3
votes
5answers
601 views

Technique for proving four given points to be concyclic?

While making my way through an exercise, I stalled on question 7: 7. Prove that the points $(9, 6)$, $(4, -4)$, $(1, -2)$, $(0, 0)$ are concyclic. The book does not provide any guidance on how ...
0
votes
0answers
8 views

Kiselev's Book I Plainimetry Question 242 - Question in the Description

Two lines passing through a point Μ are tangent to a circle at the points A and B. Through a point С taken on the smaller of the arcs AB, a third tangent is drawn up to its intersection points ...
1
vote
5answers
55 views

Dartboard puzzle.

Given a dartboard of radius r and infinite darts.How many minimum darts you need to throw so that you can be sure that the next dart you throw is strictly less than r distance from some previous dart? ...
1
vote
1answer
47 views

Geometry question, prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$

I got the following question: Prove that $\angle APB = \frac12 (\angle AMB + \angle CMD)$, with the following figure given: Also, the following information is given: $M$ is the centre of the ...
0
votes
1answer
437 views

Calculus Riemann sums for circle and ellipse

I ran into this problem today. I need to compare the Riemann sums for a circle and an ellipse. I have no idea as where to start. Here's the question:
2
votes
2answers
8k views

Calculating a circles radius from two known points on its circumference

For a simulation, I need to be able to calculate the radius $r$ of a circle $C$, knowing only two points on its circumference, $P_1$ and $P_2$, as well as the distance between them ($a$) and how much ...
1
vote
2answers
415 views

Bounding box enclosing circles, that complies with ratio constraints

Given a circle centered at $A$, with radius $R_a$ and another radius $R_b$, I need to find a center for circle $B$ such that both circles are tangential, and the bounding box including both circles ...
1
vote
1answer
295 views

Intersection of a point and absolute value function contained within a circle

I'm attempting some crazy ideas while programming a game and ran into the following math problem that has been bugging me for a few days: Given a unit circle and a random point $P$ within the circle, ...
6
votes
1answer
570 views

Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
1
vote
1answer
37 views

Maximum number of equilateral triangles in a circle

I am stuck with a question. Given a circle with radius $x$ cm, what is the maximum number of equilateral triangles of side length 1 cm that can fit in the circle without overlapping or ...
0
votes
0answers
11 views

polar moment of area for nonplaner circle (cup)

Can somebody tell me the polar moment of area of chord for a sphere. for example when you cut a sphere at a point other than from center? Also polar moment of area for curved axis symmetry ?
0
votes
2answers
47 views

Two circle intersection: help on understanding a specific explanation

As someone with basic algebra knowledge, I am having trouble understanding Paul Bourke's explanation on "Intersection of two circles" on this page. The specific part that I don't understand is where ...
0
votes
2answers
140 views

Distance from the midpoint of a radius to another point on the same radius

Here is a picture of the problem. Note that $M$ is the midpoint of $OB$. How do I figure out what $MH$ is?
3
votes
1answer
82 views

Calculating angle on ellipse

This is a really basic question, yet I can't remember my old geometry classes nor could I find an answer via google. Given a circle "tilted" at angle a to the horizontal plane, and given angle b ...
0
votes
1answer
44 views

Finding all intersecting circles of one circle.

I have one circle $C_0(x_0,y_0,R_0)$ in a plane (which moves around here and there). There are many other circles on the same plane $C_1(x_1,y_1,R_1),C_2(x_2,y_2,R_2).....,C_n(x_n,y_n,R_n)$ where ...
0
votes
0answers
10 views

Shear Stress of Circular non-planer plate

Shear Stress of plan circular plate is given by T = M/($2*t*$Pi*r^2) What will be Shear stress of non-Planer circular plate? For example chord of shpere or any other circular plate but curved in ...
-2
votes
1answer
30 views

Finding a point along a circle a certain distance away from another point [closed]

How do I find the point(s) C (and C') which: lies on a circle centered at a point B with radius r is at distance d from point A A specific case would be: A = (0,0) B = (5,7) r=5 d=5
1
vote
1answer
33 views

Surface area of circle extracted from a tube wall

I have made a hollow tube (thickness $1$mm) having inner radius $89$ mm and outer radius $90$ mm (length $400$ mm, can be higher). then I made a circular (circle radius $25$ mm) cut perpendicular to ...
4
votes
1answer
1k views

Find the radius of a circle based off of its intersection with another

So I have some circles that look kind of like this: I'm given the radius of the circle with center point $A$ which is also the distance $AB$, the distance $AB$ between the two center points on the ...
1
vote
2answers
1k views

area of shaded region in circle

Solution : $\angle O = \angle D = \theta$ (corresponding angles) Also we can use area of sector formula After that, I have no idea
0
votes
1answer
69 views

Triangle construction procedure

Two lines $L1,L_2$ pass through a common point $O. $ $L_2$ goes through points $P$ and $Q$. How to construct a circle through $P,Q$ to be tangent to $L_1?$ In a particular case, at the tangent ...
1
vote
0answers
30 views

How many discs necessary to cover a big circle?

Let be a circle a radius R,and other discs of radius r,palpable. I can cover the circle,completly, with a minimum number of discs,N.I can't cut any disc. What is the value of N,according to R and r? ...
0
votes
2answers
27 views

Intercept made by a line between two concentric circles

Let $$x^2+y^2-9=4r^2\enspace (r=1,2,3)$$ be $3$ concentric cirlces. Prove that the intercept made by line $$3x+4y+15=0$$ between any two cirlces is same. I thought of calculating the intercept ...
5
votes
1answer
62 views

Arranging circles around a circle

$N$ circles are given by their radii: $r_1$, $r_2$,..., $r_N$. They are arranged around another circle so that they pack, like in this picture (order of $N$ circles should be preserved): What is ...
2
votes
4answers
104 views

Maximum area of a rectangle

Two concentric circles have radii 13 and 15. Let ABCD be a rectangle, so that A and B lie on the larger circle, and C and D lie on the smaller circle. Find the maximum area of rectangle ABCD. I tried ...
1
vote
3answers
1k views

Triangle inscribed in circle, vertex at circle's center, solve for unknown angles.

$O$ is the center of the circle , $A$ and $B$ lie on the circle what are the possible values of $x$ and $y$ I found answers options , asked to mark one or more ...
1
vote
2answers
41 views

Simple question about circles.

Let's say I have a set $S=\{(x,y): x^2+y^2=1\}$. I want to prove that for every $i \in [-1,1]$ there's a point $(i,y) \in S$. I know this sounds pretty trivial, but I need this fact for a another ...
1
vote
2answers
45 views

A Part of a semicircle between the two legs of a right angle triangle

In a right angled triangle, a semicircle is drawn such that its diameter lies on the hypotenuse and its center divides the hypotenuse into two segments of lengths 15 and 20.Find the length of the arc ...
1
vote
1answer
24 views

How to get circle points in 3d given a radius and a vector orthogonal to the circle area?

I already know how to get a point on a circle (here), but I need a circle in 3d which should be the orthogonal to a given vector. I got: Angle in degree/radians Circle radius Orthogonal vector I ...
2
votes
1answer
52 views

Prove that $\frac{1}{r_1}-\frac{1}{r_2}=\frac{2}{a}+\frac{2}{b}+\frac{2}{c}$

If $a,b,c$ be the radii of three circles which touch one another externally,$r_1$ and $r_2$ be the radii of two circles that can be drawn to touch these three,prove ...
0
votes
1answer
80 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 ...
1
vote
3answers
3k views

Find the length of the common chord

"Two circles with centres C1 and C2 and radius $6$ cm and $8$ cm respetively cut each other at right angles. Find the length of ...
1
vote
1answer
291 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. ...
1
vote
1answer
33 views

Prove that the length of the common chord is $\frac{2ab\sin \theta}{\sqrt{a^2+b^2+2ab\cos \theta}}$

Two circles ,of radii $a$ and $b$,cut each other at an angle $\theta.$Prove that the length of the common chord is $\frac{2ab\sin \theta}{\sqrt{a^2+b^2+2ab\cos \theta}}$ Let the center of two circles ...
2
votes
1answer
32 views

How is this circle inversion formula calculated?

I know about the inversion of a point inside a circle. But I was reading Peter Sarnak's paper on the Apollonian gasket, and got to the part where he was trying to prove descartes circle theorem. He ...
0
votes
1answer
23 views

Can someone explain this unit vector calculation for this circle inversion formula derivation?

I'm really stuck. I'm learning about circle inversion. More specifically, I was trying to understand how to derive the inversion formula for a circle, which seems to be explained here. ...
0
votes
1answer
57 views

Find the area of the shaded section on a square.

In the diagram,the curved paths are arcs of circles centered at vertices $A$ and $B$ of a square of side $6$. Find the area of the shaded section $BCD$. I've been stuck on this problem for days. I ...
2
votes
3answers
40 views

Proving a ratio that has a relation with the Perpendicular bisectors and circumcircle

$ABC$ is a triangle, $D$ is a point on the side $BC$ of $\triangle ABC$, $R_b$ is circumradius of $\triangle ABD$ , and $R_c$ is the circumradius of $\triangle ACD$. Prove that $$ {Rb\over Rc} ...
1
vote
1answer
29 views

Prove that distance of $P$ from either of the points of contact is $\sqrt{\frac{abc}{a+b+c}}$

Three circles of radii $a,b,c$ touch one another externally and the tangents at their points of contact meet at a point $P$.Prove that distance of $P$ from either of the points of contact is ...