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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2
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1answer
65 views

Does this alternating sum of roots converge to $\sqrt2$?

This problem arose from what I'm hesitant to call an investigation into a certain type of "quadrature". Starting with the unit disk, I partition it into $p$ pieces by cutting the disk with vertical ...
0
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3answers
31 views

Finding the locus of a point P if the tangents drawn from P to circle x^2 + y^2 = a^2 so that the tangents are perpendicular to each other?

I tried solving this and then I got to this condition here, after I applied the formulua for finding the angle between the tangents Formula is Angle btw tangents = cos(theta) = (1 - tan^2(theta)/2)/ ...
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3answers
40 views

Show that the circle drawn on a focal chord of a parabola $y^2=4ax$, as a diameter touches the directrix

Question: Show that the circle drawn on a focal chord of a parabola $y^2=4ax$, as a diameter touches the directrix. Let the parabola be $y^2=4ax$ Let the focal chord be $y = m(x-a) $ Subbing ...
3
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3answers
355 views

Circle Geometry Questions

In rectangle $ABCD$, we have $AD = 3$ and $AB = 4$. Let $M$ be the midpoint of $\overline{AB}$, and let $X$ be the point such that $MD = MX$, $\angle MDX = 77^\circ$, and $A$ and $X$ lie on opposite ...
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3answers
22 views

Given a tangent a radius, how can you calculate the center point of a circle? [on hold]

How can you calculate the center point (2D) of a circle knowing its radius and a tangent $y = mx + t$?
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0answers
23 views

Sum of Area of Circles. [duplicate]

A circle of radius x cm is inscribed in an equilateral triangle and is tangent at three points. Three smaller circles are inscribed so that they are each tangent to two sides of the triangle and to ...
2
votes
1answer
23 views

Dissecting a circle with an irregular rectangular grid

Can a circular disc be 'dissected' by a rectangular grid into a finite number of pieces in such a way that the individual pieces of the circle can be grouped into regions of equal area? Clearly ...
-1
votes
1answer
40 views

Find the radius of three identical circles which touch each other externally.

Three identical circles touch each other externally. The tangents at their point of contact meet at a point whose distance from any point of contact is 2 cm. The radius of the circles is?
1
vote
1answer
37 views

In the figure, two circles intersect at $P$ and $Q$…

In the figure, two circles intersect at $P $ and $Q$. $O$ is the centre of the smaller circle which lies on the circumference of the larger circle and $RO$ is joined and produced to meet $QS$ at $X$. ...
2
votes
6answers
47 views

Choosing a value so a line and circle intersect a one, two, and no points

Let l be a line and C be a circle. $y=x+d$, where $d$ is to be determined. $C=x^2+y^2=4$ Pick a value for $d$ so that l and C intersect at one point. Pick a value for $d$ so that l and C ...
0
votes
1answer
36 views

Find sides of isosceles triangle inside a circle with line segment lengths as 5 and 4 as shown in the link. pls help!

Pls see the diagram below. I tried to use similar triangles and came to my wits end. Any help will be appreciated!
0
votes
1answer
36 views

Problem on circles, tangents and triangles

Let $c_1,c_2,c_3$ be three circles of unit radius touching each other externally. The common tangent to each pair of circles are drawn (and extended so that they intersect) and let the triangle formed ...
0
votes
0answers
38 views

What information is needed to determine a unique circle? [on hold]

What information is needed to determine a unique circle? I've been trying to find the answer to this question, but I keep getting results about 3-point proofs, but that is not what I am looking for.
0
votes
1answer
27 views

Formula to map any given point on circumference of circle with given radius

I am working on a project where I need this. Mathematically : I need a formula to map any given point P(x,y) on circumference of a circle of given radius r and center c in 2D space. Insights of ...
-2
votes
1answer
24 views

Find the equation of a circle passing through $(-2,4)$ and through the point of intersection of a circle$\dots$ [on hold]

Find the equation of a circle passing through $(-2,4)$ and through the point of intersection of a circle $x^2 + y^2 - 2x - 6y + 6 = 0$ and a line $3x+2y-5=0$
2
votes
1answer
47 views

Largest enclosed (inscribed) circle in cloud of points

I have a set of points that approximately lie on a circle. I would like to compute the largest circle that does not contain any of the points. Of course, one could draw the circle far away from the ...
0
votes
2answers
46 views

Point A is picked randomly in a circle with a radius of 1, and center O. What is the variance of length OA?

Point A is picked randomly in a circle with a radius of 1, and center O. What is the variance of length OA? I believe the CDF has to found first, then we need differentiate it, find the expected ...
-1
votes
1answer
16 views

Find the measurement of…

Find the measurement of unknown angle in the given circle with centre at $O$. My Attempt $1$. $\angle QRS=\angle PQR$ $2$. $\angle PQR=\angle PMR$. I am struck here. Please help me with this ...
0
votes
2answers
51 views

How to find the tangency condition for this circle geometry problem?

Suppose I have a circle $C$ of radius $1$, and I have a chord of this circle, of given length $l$. The chord makes a known angle $\theta$ with the tangent to the circle. I position a smaller circle $...
-1
votes
1answer
20 views

how to get the angle of arc ??

dart game board is divided into sectors by 30 degrees like pizza slice. the given is (x, y) coordinates, and I need to find where coordinates are lying on. how can I get the angle just with ...
0
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0answers
10 views

Probability Distribution over successive circular arcs.

So I'm looking at a problem sketched out below: so here what happens is you have a particle which moves at a constant speed and has some current orientation. At each timestep it can change it's ...
0
votes
2answers
47 views

Finding Perimeter of Shape

"Two circles of radii 5cm and 12cm overlap so that the distance between their centers is 13cm. Find the perimeter of the shape." This question was from a chapter about circle measure under the length ...
0
votes
1answer
19 views

Formula for calculating x2 and y2 of a line that behaves like a clock hand?

In the image below, the diameter of the circle is 100, and x1=50 and y1=50 for the line's starting point in the middle. I'd like to be able to draw the line so that it is pointing at different ...
1
vote
1answer
43 views

Given: 2 lines containing the diameter of a circle and a point lying on this circle; Find: the equation of this circle

The lines $ y = \frac{4}{3}x - \frac{5}{3} $ and $ y = \frac{-4}{3}x - \frac{13}{3} $ each contain diameters of a circle. and the point $ (-5, 0) $ is also on that circle. Find the equation of this ...
4
votes
2answers
44 views

Area of a circle on sphere

On a (flat) Euclidean plane, the area of a circle with a radius $r$ can be described by the function $A(r) = \pi r^2.$ But how can one describe the area of the same circle on a spherical manifold? ...
-6
votes
0answers
81 views

Given 2 lines containing the diameter of a circle and a point lying on this circle, find the equation of this circle [closed]

The lines $ y = \frac{4}{3}x - \frac{5}{3} $ and $ y = \frac{-4}{3}x - \frac{13}{3} $ each contain diameters of a circle and the point $ (-5, 0) $ is also on that circle. Find the equation of this ...
1
vote
2answers
34 views

How to find the equation for the circle when…

A circle goes trough two points, $A=(-1,2)$ and $B=(3,0$). You also know that the center of the circle is an element of the following linear equation: $$k \leftrightarrow 2x+y+3=0 .$$ How can you ...
1
vote
2answers
57 views

If the circles $x^2+y^2…$

If the circles $x^2+y^2+2ax+c^2=0$ and $x^2+y^2+2by+c^2=0$ touch externally, prove that $\frac {1}{a^2} +\frac {1}{b^2}=\frac {1}{c^2}$. My Attempt Here $$x^2+y^2+2ax+c^2=0$$ $$x^2+2.x.a+a^2-a^2+...
0
votes
1answer
33 views

Find radius of circle (or sphere) given segment area (or cap volume) and chord length

The goal is to design a container (partial sphere) of given volume which attached to a plane via a port of a given radius. I believe this can be done as follows but the calculation is causing me ...
0
votes
2answers
38 views

Find the equation of a circle…

Find the equation of a circle with radius 4 units, whose Centre lies on the line $4x+13y=32$ and which touches the line $4x+3y+28=0$. I could only make a figure with the help of the question. can ...
0
votes
2answers
21 views

Finding Radius Of Circle From Circle's Equation

For basic equations like:- $$ x^2 + y^2 = 4 $$ we can find out that the radius of the circle is 2. But for an equation like:- $$ x^2 + (y+1)^2 = 1 $$ What will be the radius of the circle?
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0answers
41 views

Circles and generic implicit functions

I have some problems understanding circles. $x^2+y^2 = 1$ is a circle. It defines equivalence class where all (x,y) points belonging to the circle are in the same equivalence class. $(\cos a, \sin a)$...
2
votes
1answer
65 views

Circle Puzzle Geometry

Two friends are playing a game. One friend stands in the middle of a circle radius 100m. His objective is to leave the circle. He may take one step at a time, distance 1m, in any direction. However, ...
0
votes
1answer
46 views

How to find the area shared by 4 quadrants inside a square?

I was to find the blue area in this question : As described about how it's a square with 4 quadrants of same radius intertwined with each other, now to find the blue part area I thought about ...
1
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0answers
46 views

Cutting a pie into 2 unequal peices with a single cut, minimising its length. [closed]

Suppose we have a circle with an area of 1, which we are to cut into two pieces, of area (x) and (1-x) respectively. Let x<0.5. How should we make the cut, to minimise its length? What is the ...
3
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0answers
23 views

Cutting a pie into n equal area pieces with the minimum distance of cuts. [duplicate]

Suppose we are to cut a unit circle into n equal area pieces. We can cut curves if we wish. What is the minimum distance we must cut? What strategy minimises this distance? Note: The shape of the ...
3
votes
1answer
35 views

Area of circle segment intercepted by a line

The problem I want to solve is to calculate the filled area in the following diagram - so basically the area between the two circular arcs but with the red line cutting off one side. I think I have a ...
2
votes
4answers
127 views

Common tangents to circle $x^2+y^2=\frac{1}{2}$ and parabola $y^2=4x$

I'm having trouble with this. What i do is say $\epsilon: y=mx+b$ is the tangent and it meets the circle at $M_1(x_1,y_1)$, i equate the $y$ of the tangent with the circle: $y=\pm \sqrt{1/2-x^2}$ and ...
0
votes
1answer
39 views

Prove concurrency in a triangle

If a circumference cuts a triangle $ABC$ at its sides $BC$, $CA$ and $AB$ at points $P, P'; Q, Q'; R, R'$; respectively (so twice on each side, and if $AP, BQ$ and $CR$ are concurrent (intersect at a ...
0
votes
1answer
20 views

Spaces relations

I have a physics question for which I need to determine the radius of a circle. Given are two Ellipse shapes with the same center (0,0 in a Cartesian space). the Height and Width of the smaller is 1[...
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vote
2answers
44 views

Calculate the angle when the area of section is given as the % of total area of the circle

This is not a homework. Just a sudden mathematical spark of my brain prompted me to simply calculate this. In the diagram above the area of the hatched section is 10% of total area if the circle. ...
0
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2answers
51 views

Angle Between Two Tangents

In the picture below, the angle $AOB$ is $\delta \theta$, and then it is deduced that the angle between the two tangents is the same from the fact that the angles in a quadrilateral add up to $2 \pi$. ...
1
vote
1answer
26 views

How to find the coordinates of the points $ T$ and $T'$

Referring to the accompanying figure,how to find the coordinates of the points $T$ and $T'$, where the lines $L$ and $L'$ are tangent to the circle of radius $1$ with center at the origin.
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2answers
49 views

Calculating distance between two points on a circle in either radians or degrees

I've asked this question a couple of times but I haven't been specific enough, I think, to get to the true answer. After spending a couple of weeks trying to get to the answer to this issue I finally ...
1
vote
1answer
40 views

Inscribed Shape on Circle given Specific Edges

How would you find the vertices (corners' position) of a shape that inscribes a circle of adjustable radius, given a set of edges? Angles of polygon are not fixed, but edges are. A few examples: ...
0
votes
2answers
73 views

Compute the area of a oval based 2d geometry

I know that the area of a shape generated as below $R=r_0+a_1\cos(\theta)+a_2\cos(2\theta)+a_3\cos(3\theta)+...$ Where you can plot it and see the area value in matlab by: ...
0
votes
0answers
35 views

Lenght of a tape on “circle”

We need to know some equation about lenght of a tape if we have predefined circle radius. This tape is then wrapped over a circle. So r of a circle is for exaple 80mm, the tape is 0.05mm. So after ...
1
vote
1answer
33 views

Prove that as $PP'$ varies,the circle generates the surface $(x^2+y^2+z^2)(\frac{x^2}{a^2}+\frac{y^2}{b^2})=x^2+y^2.$

$POP'$ is a variable diameter of the ellipse $z=0,\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ and a circle is described in the plane $PP'ZZ'$ on $PP'$ as diameter.Prove that as $PP'$ varies,the circle ...
0
votes
1answer
71 views

Locus of the center of the circle of radius $a$,which always intersects coordinate axes

If the axes are rectangular, show that the locus of the center of the circle of radius $a$,which always intersects coordinate axes is $x\sqrt{a^2-y^2-z^2}+y\sqrt{a^2-z^2-x^2}+z\sqrt{a^2-x^2-y^2}=a^2$ ...
1
vote
1answer
32 views

Largest equation of a circle that shares 2 tangents with a curve

Just played around on a graphic calculator a little, and discovered that given the curve $y=x^2$ , all circles with the equations in the form of $\left(y-a\right)^2+x^2=\frac{4a-1}{4}$ for all $a>0....