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
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Finding a length (x) inside a circle sector given another length (y) and the arc length (s) [closed]

I am stuck on a problem and can not seem to find a solution, maybe someone here can help me or at least tell me if it is possible to solve? Please look at the figure: The problem is: Find the ...
2
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1answer
29 views

Questioning about the meaning of “$1$-dimensional circle”

When we talk about the $1$-dimensional circle, is it a one-dimensional object, although one can embed it into a two-dimensional object? More precisely, is it a one-dimensional manifold?
9
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2answers
93 views

How many mutually orthogonal circles are possible?

How many mutually orthogonal circles is it possible to have? It is easy to construct $3$ mutually orthogonal circles, e.g. $3$ circles with radius $1$ and centers at the vertices of an equilateral ...
2
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1answer
22 views

Find radius of a circle from intersecting chords

Say I have two chords that intersect inside a circle, not at a right angle, and neither is the diameter. It seems to me this is enough information that the circle must be unique, but I can't seem to ...
0
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1answer
23 views

Problems on measure of angles and arcs in a circle diagram

A friend of mine recommended this site. I cannot figure out any of the parts in the problem in the picture click here The line segments AE and DE are not tangent to the circle, so I don't know where ...
1
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3answers
47 views

Same perimeter and area for a circle and an ellipse

For a given circle, is there exist an ellipse with same perimeter and area as to that circle? If not, that is my suspicion, is in three-dimension parallel question: For a given sphere, is there ...
1
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1answer
24 views

Find altitude of equilateral triangle given inscribed circle dimensions and position

I've found myself trying to solve this for my Geometry class where we have to model a basic piece of architecture and find its volume and surface area (very basic). But the structure I chose requires ...
0
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0answers
16 views

compute integrals on the circle group

Let $\theta(t)\in SO(2)$, where $SO(2)$ is the special orthogonal group. I want to compute $\theta(t)$ by integrating an 'angular velocity', say $\omega(t)\in\mathbb{R}$. Hence, I want to write $$ \...
0
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1answer
25 views

A circle tangent to two circles touching internally and line

Find the radius of a circle touching two circle $x^2+y^2+3\sqrt{2}(x+y)=0$ and $x^2+y^2+5\sqrt{2}(x+y)=0$ and also touching the common diameter of the two given circles. The two circles touch ...
0
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2answers
35 views

Tangent line to quarter circle inscribed in square ABCD intersects point X. Where to start?

Disclaimer: The answer must be an integer, as all competition problems were designed to yield integral answers. Hello! Yesterday I underwent a math tournament. There was one problem that was rather ...
0
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1answer
45 views

Circles overlapping a central point

If I have a circle x with radius r. How many circles can I add around it with same radius such that these circles overlap the center point of circle x without overlapping any other circles' center ...
2
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2answers
33 views

Can a polygon with an infinite number of sides be viewed as a line?

The inner angles of a polygon approach 180º as the number of sides (N) of the polygon increases. So, if N approaches infinity, we would have a circle. But... At infinity, we would also have a set of ...
2
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1answer
38 views

Tournament of Towns Geometry Problem, Proof by Construction?

I was to prove the following proposition from an old Tournament of Towns problems archive: Problem. A circle $\omega_{1}$ with center $O_{1}$ passes through the center $O_{2}$ of another circle $\...
0
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3answers
50 views

A simple proof that a polygon circumscribing a circle overestimates its perimeter

Looking at the picture below, it's easy to see why the perimeter of a polygon inscribed in a circle is an underestimation of the circle's perimeter. This follows from the triangle inequality: Any side ...
0
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1answer
38 views

Given a chord length and distance from center find length of a different chord

A chord that is of length 18 cm is 12 cm away from the center of a circle. How far is a chord of length 10 cm from the center? I know that chord of equal distance away are equidistant from the center ...
0
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2answers
29 views

How do i compute the closest points on a sphere given a point outside the sphere?

I looking for method which can compute the yellow area in this image.. The ball with the green fill is a sphere, where i know the center point and the radius of it. The circle with the red fill ...
5
votes
3answers
49 views

Finding the Center of a circle given two points and a radius (algebraically)

Preface: I'm writing a program in which I need to find the center of a circle, given two points on the circle, and the radius. Therefore, a construction or doing the problem out by hand is not an ...
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votes
3answers
97 views

Prove that $\mathbb{S}^1$ is not homeomorphic to $\mathbb{S}^2$.

I've been able to show that $\mathbb{R}$ is connected and $\mathbb{R}^2 \backslash \{ x\}$ is connected for any $x \in \mathbb{R}^2$. Using this I was able to show that $\mathbb{R}$ and $\mathbb{R}^2$ ...
-1
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1answer
35 views

how to distance circles drawn on another circles

I need to do some calculations in order to do this drawing (sorry for the quick sketch): I need to define a set of variables and do simple calculations as much as possible in order to come up with ...
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1answer
48 views

How to calculate angle within a circle

Given this situation where the circle is cut by the rectangle. How do you calculate the angle α
0
votes
0answers
44 views

Double Integral over the region of an ellipse cut off by a circle

I've been stuck on this question for awhile. I need to calculate the double integral $\iint_R \frac{1}{r^3} dA$ using polar coordinates. R is the region displayed below: The ellipse has centre (4,...
1
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2answers
63 views

Evaluate the double integral $\iint_D\sqrt{4-x^2-y^2}$ bounded by semi-circle

I would appreciate it if someone can help me solve this question, as I'm struggling to get its answer. Q: Evaluate the double integral $$\iint_D\sqrt{4-x^2-y^2}dxdy$$ bounded by semi-circle $$x^2+y^2=...
0
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2answers
37 views

What is the relationship between the width, height, and radius of an arc?

What is the relationship between the width ($w$), height ($h$), and radius ($r$) of an arc? Specifically, the relationship in terms of $h$. I know this is a simple question - I'm a hobbyist engineer,...
4
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0answers
54 views

Archimedes Classic Proof for Area of Circle: Love it but can't grasp one aspect…

The proof assumes that:... The perimeter of any CIRCUMSCRIBED regular polygon is GREATER than the circumference of the circle. ie: !http://www.themathpage.com/atrig/Trig_IMG/eval1.gif Is this an ...
0
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2answers
34 views

How do I calculate the height of an arc?

I'm a hobbyist engineer, having one of those moments where my mind goes blank. I know this is a simple problem, but I can't remember how to approach it. I have an arc defined by width and angle. ($w$ ...
0
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3answers
30 views

Number of chords of a circle having natural length

In a circle of radius 17, point p lies on a distance 15 from center.How many distinct chords of this circle passing through p do have a natural length? I tried to use the notion of Power of point ...
0
votes
3answers
22 views

Find center of circle with 2 internally touching circles

A third circle is drawn such that: both $C_1$ and $C_2$ touch internally The centres of $C_1$, $C_2$ and $C_3$ are collinear. Determine the equation of $C_3$ Circle C1 has the ...
1
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2answers
57 views

Can $n$ circles be drawn such that all have a common intersection but no two intersect individually

I was fiddling with plane geometry when a question came into my mind: Can $n$ circles ($n \ge 3$, $n \in \mathbb{N}$) be drawn such that: $C_1 \cap C_2 \cap C_3 \cap \ldots \cap C_n \not = ...
1
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1answer
24 views

Oriented atlas on a circle

I'm trying to find an oriented atlas on the circle $S^1$, i.e., I want to find an atlas for $S^1$ such that for any two overlapping charts $(U,s)$ and $(V,t)$ of the atlas, the derivative $d s/d t$...
-1
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1answer
15 views

How To Calculate Start and End Points on a curve and Locate the Center

I am working on an irregular polygon. What I am trying to calculate is the center location of the arc and where the start and end points of the arc are located. I am working in AutoCAD so I can draw ...
0
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1answer
40 views

circle cuts three circles at the extremities of the diameter

If the circle $$x^2 + y^2 + 2gx + 2fy + c = 0$$ cuts the three circles $$x^2 + y^2 – 5 = 0\space;\space x^2 + y^2 – 8x – 6y + 10 = 0 \space;\space x^2 + y^2 – 4x + 2y – 2 = 0;$$ at the ...
0
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0answers
19 views

$(x-1)(y-2)=5$ and $(x-1)^2+(y+2)^2=r^2$ intersect at four points $A,B,C,D$. Centroid of $\Delta ABC$ lies on $y=3x-4$, then the locus of $D$

$(x-1)(y-2)=5$ and $(x-1)^2+(y+2)^2=r^2$ intersect at four points $A,B,C,D$. If centroid of $\Delta ABC$ lies on $y=3x-4$, then what is the locus of $D$? I did try a couple of things, but I honestly ...
0
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4answers
59 views

How to calculate the radius of a circle inside a hexagon?

If I know how big is one side of a hexagon, what's the formula to calculate the radius of a circle inside it?
1
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2answers
31 views

Find a point on a circle given a point and height

Point on a circle Given : A point on a circle (point and angle), radius of the circle , height (Orthogonal to horizon ) I would like to find A point on a circle or , and The angle between the ...
0
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2answers
53 views

2 circles in an isosceles triangle

I've been given the following school problem: ABC is an isosceles triangle (AB = AC). The radius of the incircle is R and of the other circle (which is tangent to the incircle and to the legs of ...
1
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2answers
21 views

Proving the Secant Angles in the Circle

Ok, I know this is a very easy circle geometry problem, but I want to know that how to prove the theorem of angles in the circle. Like this image here: How can I prove that the angle $X$ is the ...
2
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1answer
26 views

calculate circle cardboard segments

I want to make a cardboard lamp, but i want it to look like half a sphere. Given a cardboard thickness of x, and a circle width of y, how many elements do I need and what radius do the elements need ...
-1
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1answer
26 views

Question on circles…

If three circles with radii ${3}$,${4}$,${5}$ touch each other externally at points P,Q and R,then the CIRCUMRADIUS of ∆PQR is...?? My attempt i think that the let the point of the common ...
1
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1answer
23 views

find the equation of the diameter which passes through the origin.

I am given the equation of the circle $x^2+y^2−4x+6y=14$, and I am told to find the equation of the diameter which passes through the origin. However, I am unsure as to how to do this.
2
votes
1answer
27 views

What is the minimum radius $r$ of two intersecting circles that are spaced $x$ apart that completely enclose a square of length $w$?

Let's say we have two circles whose centers are spaced a fixed $x$ units apart from one another. Both circles have a radius $r$. Our goal is to identify the minimum value of $r$ so that the ...
0
votes
1answer
40 views

Proving three points lie on a same line

Given two circles $C1$ and $C2$ how do I prove that the line joining their centers will pass through the point of intersection of their internal common tangents.I tried to form a linear pair and prove ...
0
votes
1answer
35 views

Find length of a chord of a circle with radius $13$ cm given position of a point located on the chord.

A point located on a chord of a circle is 8 cm from one endpoint of the chord and 7 cm from the center of the circle. If a radius of this circle is 13 cm long, how long is the chord, in cm? Please ...
2
votes
3answers
73 views

Straight Edge - Only Geometric Construction

Given a circle, its diameter and a given point on the diameter, find a procedure to construct a line perpendicular to the diameter using only a straight edge. The perpendicular must pass through the ...
0
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2answers
36 views

Intersection of two circles giving reversed answer

A little help needed. I need to derive the formula for the intersection points of two random circles. Equation: $\ x^2 + y^2 = 2.4^2$ and $ x^2 + (y+4)^2 = 17.16 $ I derived the equation which ...
3
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2answers
104 views

Construction using a straight edge only

Given a circle, its diameter and a point on the circle, find a procedure to construct a line perpendicular to the diameter using only a straight edge. The perpendicular must pass through the given ...
0
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3answers
36 views

How to check if two circles have common part?

I have equasion to calculate area of two circles with common part. Equasion common part But actually I just need to know if two cirlces have common part or no. Is there simpler equasion for that ...
1
vote
2answers
48 views

Power of a point proof

I found the question on page 13 of this link. Let $P$ be a point inside a circle such that there exist three chords through $P$ of equal length. Prove that $P$ is the center of the circle. I ...
2
votes
1answer
89 views

Construct a circle passing through a point $X$, which is externally tangent to two given circles

Given two disjoint circles $S_1$ and $S_2$, and a point $X$ external to both of them, is it possible to find the center of a circle that passes through $X$ and touches $S_1$ and $S_2$ tangentially, ...
0
votes
2answers
47 views

Geometry experts! Three equal tangential circles: What is the ratio of the blue line to the red line?

Consider the three tangential circles of equal radii inscribed in the equliateral triangle (linked to below). What is the ratio of the blue line to the red line? The red line is simply the diameter ...
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2answers
32 views

Prove $∠ADM = ∠ACB$ of triangle $ABC$ [closed]

Suppose that $ABC$ is a triangle. Let $D$ be its circumcenter and let $M$ be the midpoint of $\vec {AB}$. Show that $∠ADM = ∠ACB$.