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

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0
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1answer
27 views

Calculating the length of a tangent drawn to a circle from a named point

My book (New Tertiary Mathematics Volume 1 Part 1, by C Plumpton and P S W Macilwaine) describes a method for calculating the length of a tangent to a circle from the point $(x_{1}, y_{1})$ outside ...
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0answers
20 views

Find the sub-area of a circle cut by chords [on hold]

Suppose a circle of area $A$ is given, and then cut off portions using chords of the circle. What is the resulting area based on such chords?
8
votes
1answer
145 views

Can the $9$ point circle be generalized to $n$-gons of $n\gt3$?

All triangles have concyclic vertices and have a $9$ point circle which intersects the triangle's feet and the midpoints of its sides (as well as $3$ other significant points). Is this special for ...
0
votes
1answer
518 views

Geometry Find the Radius of a circumcircle given the area of the triangle

Ok so here is what I know, the circumcircle of an equilateral triangle with an area of $4\sqrt{3}$ is drawn, calculate the radius lenght of the circumcircle. I also know that to find the radius I ...
0
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0answers
29 views

Formula for area of circle made up of squares

I need to draw an approximate circle on a grid of squares and find its area. Each square must either be completely part of the circle or not at all occupied. Obviously, this means that it cannot be a ...
1
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0answers
39 views

2015 AMC12A question 25

This is a question from the 2015 AMC12 math competition. I haven't really made much progress at all on it, and I just want to know the right way to solve this equation. A collection of circles in ...
2
votes
1answer
39 views

Does this equation for a tangent to a circle have a name?

My Maths tutor showed me a shortcut way to find the equation of a tangent to a circle, given the radius, centre and point the tangent touches the circle: $$(x - a)(c - a) + (y - b)(d - b) = r^2$$ ...
2
votes
3answers
50 views

Find circle radius by given triangle inside

So the triangle inside the circle: $AB = 9$cm $CB = 6$cm $CH = 5$cm I think solving this problem involves similar triangles. Thanks in advance, I'd like to have a solution suitable for 9th ...
1
vote
3answers
308 views

Geometry problem on circles from a competition

Triangle $\triangle ABC$ is an equilateral triangle whose side is $16$. A circle meets the sides of the triangle at $6$ points: it intersects $AC$ at $G$ and $F$ and $|AG|=2$, $|GF|=13$, $|FC|=1$. ...
3
votes
2answers
799 views

Prove using integration that $polygon → circle\space \text{as}\space number\space of\space sides → infinity$

Say we have a regular polygon $s$, with number of sides $n$: Is there a way to prove that as $n → ∞,\space $then $s → circle$ using integration?
2
votes
1answer
46 views

Subtracting equations of two circles which don't intersect

Suppose you subtract the equations of two circles that do not intersect. In doing so, you will obtain a line which is an "extraneous solution set". Is there any geometric significance to this line? ...
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0answers
12 views

Find ArcLength given a set of circle parameters.

I need an equation to help define a 3D curve, given starting vector, ending vector, starting point, and vertical distance between start and end points. The curve should be a segment of a circle ...
6
votes
1answer
506 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
22 views

Finding coordinates of the third point of a triangle from given?

In ABC triangle we know the coordinates of A and B vertices. We also know lengths of 2 edges shown in the picture and the third edge is calculatable. What is the most efficient functon to find x3 and ...
1
vote
2answers
31 views

Circular measure

Hi everyone, This is a question from a June 1984 cambridge past paper. I'm getting stuck with the part (c) and the 'hence show...' Please someone can help, I'd be very grateful.
2
votes
2answers
103 views

A question about 4 concyclic points

In a triangle $ABC$, let $I$ denote its incenter. Points $D, E, F$ are chosen on the segments $BC, CA, AB$, respectively, such that $BD + BF = AC$ and $CD + CE = AB$. The circumcircles of triangles ...
4
votes
2answers
120 views

Three circles having centres on the three sides of a triangle

NOTE: I would appreciate it if you provided a hint and not the whole solution. BdMO 2014 Nationals: In acute angled triangle ABC, considering a portion of side BC as diameter a circle is drawn ...
2
votes
2answers
118 views

Beautiful triangle problem

Circle, inscribed in $ABC$, touches $BC, CA, AB$ in points $A', B', C'$. $AA' BB', CC'$ intersect at $G$. Circumcircle of $GA'B'$ crosses the second time lines $AC$ and $BC$ at $C_A$ and $C_B$. Points ...
4
votes
1answer
84 views

Nine-point circle equivalent for tetrahedrons?

Nine-point circle for a triangle is defined as the circle that passes through: the midpoint of each side the foot of each altitude the midpoint of the line segment from each vertex to the ...
8
votes
1answer
96 views

Characterization of the circle within metric spaces

There are various characterizations of the circle. To be precise, there is not the circle. There are several categories which contain an object we refer to as "the circle". In $\mathsf{Top}$ the ...
0
votes
2answers
629 views

Software to draw easily sectors with angle on it

I want to draw a sector with the angle on it. I have tried several tools but didn't find any easy way of doing it.
1
vote
1answer
12 views

How can I find the inner limit of a line passing through a lune?

I have a crescent defined by two offset circles with different radii: a small one (let's call it outer circle) centered at (0,0) with radius ...
1
vote
1answer
47 views

Prove that $\int_0^x \ 1/\sqrt{1-x^2} dx$ is equal to length of unit circle arc?

How to prove that $\int_0^x \ 1/\sqrt{1-x^2} dx$ is equal to length of unit circle arc? I know that the integral is $\arcsin(x)+c$ but really do not see how this is related to arc length.
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3answers
48 views

Proving algebraic equations with circle theorems

I got as far as stating that OBP=90˚ (as angle between tangent and radius is always 90˚), and thus CBO=90˚- 2x. CBO=OCB as they are bases in a isosceles. COB=180-90-2x-90-2x. But after this, i am ...
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0answers
15 views

Find The MidPoint Coordinates Of An Arc Given The Following [closed]

Coordinates of arc starting point, arc ending point, center of arc, plus values of starting angle, ending angle, sagitta, chord, and radius. Givens: Arc is entirely within the first quadrant. Arc ...
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1answer
24 views

Help with precalc homework | circles and radians [closed]

Hi everyone, i need help with my homework, ive been trying to find out the answers for the last 2 questions but ended up with nothing, please help.
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0answers
26 views

Circle Geometry

How do you derive the equation of a circle $(x−a)^2+(y−b)^2=r^2$ if a point on the y-axis is chosen as then you cannot form a triangle and as a result not apply Pythagoras' theorem and derive the ...
2
votes
1answer
209 views

Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to ...
0
votes
1answer
293 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:
0
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0answers
35 views

Probability density function for distance between two points.

Two points are chosen randomly inside a circle (and even on the circumference) with radius $r$ What is the probability density function of the distance between the points? I would be very grateful.
0
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2answers
31 views

Highschool Geometry: Finding Common Tangent

I can't seem to identify what the arrows are indicating in this question, obviously the two lines are parallel but what does it mean? I don't know where to begin. Any suggestions?
2
votes
1answer
51 views

Intersection of two circular arcs with same center [closed]

How do you programmatically get intersection points of 2 circles given the same centers, radii, and sweep angle? The 2 circles are not exactly one whole circle. I have an equation for each circle: ...
0
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2answers
37 views

Calculating if a point is within the overlap of two circles

Two circles of equal radius (R) intersect as shown below. Assuming more points are uniformly distributed in an area with dimensions D*D, where D = 4*R. What is the probability that a point will be ...
0
votes
1answer
18 views

Terminals and co-terminals for angles

I'm trying to understand how my teacher converted these angles. I'm not sure if my title is correct but I'm assuming that's what he was doing. For a unit circle he had, \begin{align*} u & = ...
0
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0answers
23 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.
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2answers
350 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
62 views

Algorithm - Circle Overlapping

Say you have a shape you want to fill up with circles, where by the circles overlap just enough to cover the whole surface area of the shape. The circles will remain as a fixed size however the shape ...
0
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0answers
14 views

How do we sketch the ellipse determined by $T(\vec{x})$ and determine its axes, given an expansion factor?

I have been told that if $\left\{\exists \, T(\vec{x})^{-1}\mid T(\vec{x})=A\vec{x} \mid \mathbb{R}^2\mapsto\mathbb{R^2}\right\}$, then the image $T(\Omega)$ of the unit circle $\Omega$ is an ellipse. ...
5
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1answer
42 views

Fitting a circle

Given a figure like , how can I determine the radius of the circle with middlepoint H analytically? CDFE is a square with sides 6/5, with E and F being points on the circles with radii 2.
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0answers
41 views

Help with this coordinate geometry question involving cirlces and parabolas.

Question: A point $P$ in a plane moves such that it remains at a fixed distance $r$ from a fixed point $A\equiv(r,r)$. (i) Find the equation of the locus of point $P$ (in terms of $r$). Another ...
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0answers
24 views

How to get points of lines tangent to 2 circles

How do you get the points of lines tangent to two circles, where both starting point and end point of line are exactly touching their respective circles? Please help. Thanks
2
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2answers
31 views

How to calculate radius of a spherical surface having four circles touching one another?

There are four circles having radii $r_1, r_2, r_3 $ and $r_4$ touching one another on a spherical surface of radius $R$ (as shown in the picture below, four colored circles touching one another at 6 ...
1
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1answer
25 views

Find point inside circle but outside of n- other circles

There is one green circle and 0 to n red circle(s). I'm trying to find a point inside the green circle, but outside all red ...
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votes
0answers
24 views

Arc subtended by inner infinitesimal angle

I am trying to find the length of the bolded arc: Assume $\theta$ is infinitesimally small, $r_A$ is the distance from the point of intersection of the chords to the point of contact of the tangent ...
1
vote
1answer
62 views

Find circumcenter when distance between ABC points of triangle with two points's ratio given

The complete problem is: I am having three points A,B,C whose ratio of the distances from points (1,0) and (-1,0) is 1:3 each. Then I need the coordinates of the circumcenter of the triangle formed ...
2
votes
2answers
342 views

Determine Circle of Intersection of Plane and Sphere

How can the equation of a circle be determined from the equations of a sphere and a plane which intersect to form the circle? At a minimum, how can the radius and center of the circle be determined? ...
1
vote
1answer
67 views

What are the distances from a line to the tangents of a circle?

I have a line given by two points, and a circle given by its origin and radius. I need to find the perpendicular distance between the line and the two tangents of the circle that are parallel to the ...
0
votes
2answers
18 views

Interpolate/Increment Vector Rotation

For my 2D physics engine, I'm using the unit vectors of the direction an object is facing to represent its orientation; essentially, [Cos(theta),Sin(theta)] where theta is the object's rotation in ...
-1
votes
0answers
29 views

External Cirlces [duplicate]

For two circles (with centres $(a_1,b_1),(a_2,b_2)$ and radius $r_1,r_2$ respectively) touching externally and the tangent at their common point passing through the origin, I have shown that $(a_1^2 ...
0
votes
1answer
20 views

Central angle of a circular sector from area and arc length

I've been doing a task which says the following: Area of a circular sector is $3.2\pi cm^2$, arc length is $0.8\pi cm$. What is the central angle? I've been attacking this from several angles ...