1
vote
2answers
31 views

Radius of a curvature

I have a lens (magnifying glass) and I want to calculate the radius of the curvatures on its sides. The lens in question diameter of the lens = 6 cm thickness at center = 7 mm thickness at edge = ...
0
votes
1answer
26 views

length of secant line.

I'm looking for way to find the length of a secant line intersecting another line through the center of a circle with a known radius. The intersection point is on the circle and the angle between 2 ...
0
votes
1answer
42 views

Inscribed Circles in Triangles

This question appeared in this year's UNSW Maths competition. It was question 5b and it was the only question that i couldn't do. Sorry if my explanation is bad as it is complicated to understand ...
0
votes
3answers
34 views

Finding the variable of a coordinate point on a circle

This might be a very simple question but I am having trouble figuring it out, so if anyone can explain: A circle is marked with three points A(-3,2),...
1
vote
2answers
22 views

Finding the points where a circle intersects an axis

A circle has the equation: x²+y²+4x-2y-11 = 0 What would be the coordinates of the points where the circle intersects with the y-axis and how would you calculate it?
0
votes
0answers
41 views

Finding circle which touches two functions

I wasn't sure whether my issue is with my Mathematica code or the actual way I am trying to figure out my problem so if it is a Mathematica issue I can ask it on that stack exchange. Firstly I have ...
0
votes
2answers
46 views

Intersection of circle and ellipse

I'm looking for the points of intersection of a circle $x^2 + y^2 = r^2$ ($r$ is known, origin is $(0,0)$) and an ellipse $(x - x_0)^2 / a^2 + (y-y_0)^2 / b^2 = 1$ ($a,b,x_0,y_0$ are known). ...
0
votes
1answer
48 views

Distance to the perimeter of a circle with given radius, distance traveled from origin, and direction

I am programmer by trade but am running into some trouble with a geometry problem. I basically want to start at the center of a circle, travel any distance within the radius, turn any direction, and ...
-1
votes
1answer
54 views

Find area of shaded region in circle

I am working on this SAT question. Progress AD = 3 largest radius =3 second largest = 2
3
votes
2answers
21 views

Circle Line segment intersection

I have a circle with radius r and center $(c_x, c_y)$. I have a line segment $(x_1, y_1)$ and $(x_2, y_2)$ given $(x_2, y_2)$ is always a point inside the circle. I am trying to find the ...
1
vote
1answer
33 views

Work out center of a partial circle

If I have a small section of a circle, inside a square. I know the height and the width of the square and therefore the width and height of the arc, what would be the quickest (not necessarily the ...
4
votes
1answer
39 views

Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$?

We are on $\Bbb{R}^2$. Let $A_1,\cdots,A_n$ be $n$ points on the unit circle. Can we find a point $M$ on the unit circle such that $\prod_{i=1}^n MA_i=1$ ? ( of course I mean the distance ...
1
vote
4answers
54 views

Circle - finding the equation

Question: Find the equation of a circle whose center is in the first quadrant; touches the x-axis at (4,0) and makes an intercept of length 6 units on the y-axis. I am getting a faint idea where to ...
1
vote
1answer
27 views

Can any vertex of an isosceles triangle represent the centre of a circle, and the base vertices represent points on the circumference of that circle?

This question occurred to me doing this circle geometry problem, and I was wondering if anyone could clear it up. Geometrically, it seems it would make sense, provided that 2 sides are equal (equal ...
1
vote
1answer
36 views

Outer interval of circle intersection

Is there a consistent way to calculate the outer interval $\left(~\mbox{element of}\ \left[0, 2\pi\right]~\right)$ of a circle created by an intersection ?. I calculated the intersection points and ...
2
votes
2answers
224 views

Finding the position of a moving point [closed]

A point is moving on a given curve. For example, curve equation is: $$x^2 + y^2 - 10y = 0,$$ which is a circle with $5$ meter radius. If point is on $(0,0)$ at $t = 0$ and is moving on the curve ...
0
votes
3answers
47 views

Finding formula for an arc of a circle that fills a rectangle

I'm working on a program where I need to draw an arc in a rectangle fulfills these requirements: 1) The arc must be part of a perfect circle (not the band!), must not be oval 2) The arc intersects ...
1
vote
2answers
23 views

Problem of bodies in motion in circles.

Consider two circles of radii $4\;cm$ and $8\;cm$, respectively, both circles have the same center $C$ and is two bodies $A$ and $B$, so that $A$ is smaller circumference of the trajectory at a ...
1
vote
2answers
29 views

calculate circle segment area: determine distance

I have a problem calculating the area of a circle segment. I know how to separate this into smaller tasks (triangle and remaining circle segment) that are basically easily solvable, but one distance ...
0
votes
1answer
27 views

Minimal number of points to define a rotated ellipse?

What is the minimal number of points $N$ to uniquely define the semi-major axis $a$, the semi-minor axis $b$ and the rotation angle $\omega$ of an ellipse whose the center is known/fixed (this is ...
0
votes
1answer
43 views

Number of triangles formed by all chords between $n$ points on a circle

We have $n$ point on circumference of a circle. We draw all chords between this points. No three chords are concurrent. How many triangles exist that their apexes could be on circumference of ...
1
vote
1answer
45 views

problem about length of perpendicular chords

Question $AB$ is chord of circle $O$,points $D$ and $E$ are chosen on $AB$ in a way that $AD=BE$.prove two chords that are perpendicular to $AB$ and pass $D$ and $E$ points are equal.(prove $LK=MN$) ...
1
vote
2answers
47 views

Geometry : find the points of tangency between two lines and two circles [closed]

I have a programming problem. I need to find the intersection points between two lines tangent to two circles and the circles! I have the circles' radiuses and centers. So I need points ...
0
votes
2answers
55 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
2
votes
1answer
36 views

How to embed this circle tangent to the other circles?

I want to construct a circle that would be tangent to the $3$ circles and would have its diameter lie somewhere on the segment $BI$. $EF$ includes the diameters of the $3$ given circles. $EB=BF$. ...
5
votes
1answer
51 views

Circle with perpendicular chords

A blue circle is divided into $100$ arcs by $100$ red points such that the lengths of the arcs are the positive integers from $1$ to $100$ in an arbitrary order. Prove that there exists two ...
3
votes
2answers
46 views

Do the centroid of a unit n-hemisphere and that of the whole n-sphere coincide when $n \to \infty$?

It is known that the distance between the centroid and the center of a unit semicircle is $\displaystyle\frac{4}{3\pi}$, whereas that of a unit hemisphere is $\displaystyle\frac{3}{8}$. I am ...
1
vote
2answers
36 views

Find the radius

Consider the parabola $y=x^2$ and a circle which is tangent to the parabola at the points $(1,1)$ and $(-1,1)$.Find the radius of circle. My try:I write the general equation of circle ...
2
votes
2answers
32 views

Calculate the closest point to the center of a circle from another circle on its radius.

There are 2 circles, the smaller one has its center on the bigger circles border, from that how can you calculate the coordinates the closest point on the smaller circle to the center of the bigger ...
2
votes
2answers
61 views

Primary school math regarding circles [closed]

----------//-----------------------------------__________ Please see the figure below the question is in the ...
2
votes
0answers
39 views

Packing circles in circle vs semicircle vs quarter of circle

Consider $N$ disjoint circles with radius $1$ packed into a larger circle $C$. Let $R$ be the smallest possible radius of $C$, allowing the best packing density. Now take the $N$ unitary circles ...
40
votes
17answers
2k views

How to create circles and or sections of a circle when the centre is inaccessible

I am doing landscaping and some times I need to create circles or parts of circles that would put the centre of the circle in the neighbours' garden, or there are other obstructions that stop me from ...
8
votes
5answers
283 views

Tangent and angle bisectors [closed]

The tangent to the incircle of a triangle ABC is reflected about the external angle bisectors. Show that the triangle formed by the resulting 3 lines is congruent to ABC .
2
votes
1answer
34 views

Calculating a specific point on a circle

I am looking for a formula to calculate the point of intersection where the arc crosses the angled line (designated by the letter 'X' in the example below), only from the dimensions given. I am ...
0
votes
1answer
35 views

Circles and tangents

3 circles of radius 3 cm, 4cm, 5 cm touch each other externally at $A$, $B$, $C$. Tangents drawn at $A$, $B$, $C$ intersect at $P$. Find $ PA + PB + PC$ . Thanks. My thoughts and approach: ...
-1
votes
1answer
94 views

What proportion of the circle is covered by the square?

Or what is the combined area of the circle segments (chords)? Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the ...
0
votes
2answers
46 views

How can I find the smallest enclosing circle for a rectangle?

I have the four vertices of a rectangle. I need to find it's smallest enclosing circle. For example: I need to find the radius of the circle.
4
votes
1answer
140 views

Find if a point lies in all given circles

I have a set of n given circles. I want to find that if there exists at least one point that lies in all of the given circles. Is there a method to do so? I can ...
2
votes
2answers
34 views

Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
2
votes
3answers
41 views

Diameter of a circle using 3 nonlinear points

I am trying to find the diameter of a circle using 3 points on its circumference. 2 of the points are 5 feet from eachother while the third point is centered between the other 2. The ceter point is ...
0
votes
1answer
30 views

The surface area of a ring: $\pi[(r+dr)^2 - r^2]$ or $2\pi r\,dr$?

I know this may be really simple but here it is nonetheless. Let's say that I have a ring with a radius of $r$ and width of $dr$. I'm trying to find the surface $dS$ of the ring. Isn't it $dS = ...
0
votes
0answers
23 views

Position vectors of sphere/circle touching central one

I am trying to understand the meaning of an expression describing the "kissing" number problem. On Wiki, it states the following: Let $x_n$ be a set of $N$ $D$-dimensional position vectors of the ...
1
vote
2answers
56 views

Locus of vertex of triangle moving inside circle

A right triangle with sides $3,4$ and $5$ lies inside the circle $2x^2+2y^2=25$. The triangle is moved inside the circle in such a way that its hypotenuse always forms a chord of the circle. The locus ...
3
votes
4answers
85 views

True or False: The circumradius of a triangle is twice its inradius if and only if the triangle is equilateral.

Let $R$ be the circumradius and $r$ be the inradius. The if part is clear to me. For an equilateral triangle, the circumcentre, the incentre and the centroid are the same point. So, by property of ...
2
votes
1answer
43 views

The locus of centre of circle tangent to two given circles

What is the locus of the centre of circles that are tangent to two given circles? I had no idea how to approach the problem so I considered a special case, namely one in which the two circles were ...
0
votes
1answer
71 views

finding points with maximum distance between them on a circle

I'm a computer science student working on a problem in computer graphics and looking for a formula that can find the x and y positions of a set of N points on the surface of a circle so that the ...
0
votes
3answers
80 views

Please find the radius of the circle.

Hello, I want to find the radius of red circle. I tried it with several ways like trigonometric. But there is a special value is given with this. I can not understand why it is given. It is the blue ...
2
votes
2answers
69 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 ...
2
votes
1answer
40 views

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through

From any arbitrary point $P$ on $y =\cos x$ tangents $PA$ and $PB$ are drawn to a circle which passes through the points $(1,0)$ and $(3,0)$ and touches the circle $x^2+y^2-2x-8=0$ and have its ...
1
vote
0answers
23 views

The Biggest Smallest Piece to Smallest Biggest Piece ratio of a circle cut by n chords with maximal number of regions

It is well known that a circle cut by n chords gives at most (n^2 + n + 2 )/2 regions eg. http://mathworld.wolfram.com/CircleDivisionbyLines.html Questions:- How close to equal area regions can we ...