1
vote
1answer
30 views

Intersection of an $n-$sphere and a plane (when non-empty and not a point)

Let the n-sphere of radius $r$ centered at $(0,0,...,0,y)\in\mathbb{R}^{n+1}$ be defined by $$ \mathcal{S} \iff {x_1}^2 + {x_2}^2 + ... + {x_n}^2 + (x_{n+1}-y)^2 = r^2 $$ and consider the function $d$ ...
2
votes
3answers
73 views

Finding circumcentre

Tangents are draw from $P(2,3)$ to $x^2+y^2=4$ meeting at $Q,R$ on circle. Parallelogram $PQSR$ is completed. Find the circumcentre of triangle $QSR$. My attempt: Clearly, the parallelogram is a ...
1
vote
1answer
25 views

Is there another way to solve the value field of a parameter of an line.

Assume $P$ is a point in line $x+y=m$, where $m \in \Bbb{R}$. There are two points $A,B$ in circle $$x^2+y^2 = 10$$ such that $PA$ and $PB$ are tangent lines of the above circle. If line: $x+y=m$ has ...
0
votes
1answer
34 views

Geometry/Trigonometry Homework Help - Circles

Help on this math problem: A regular Octadecagon (18 sides), each of whose sides are 14 inches, is inscribed in a circle. Find the radius of the circle, the size of each arc subtended by a side of ...
3
votes
1answer
38 views

Locate a point a given distance from another point on an ellipse

Similar to Point on circumference a given distance from another point, but for an ellipse. Unfortunately, the difference is non-trivial. I have an ellipse and a point (C) that is somewhere on the ...
0
votes
1answer
24 views

fixed length random chord outside of circle.

consider a uniform distribution on a unit circle, I construct a cord by the following steps: pick one endpoint A within the unit circle uniformly. points that are $0<d<1$ distance away from ...
1
vote
1answer
34 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...
0
votes
1answer
28 views

A circle is inscribed inside a sector of a circle. Given the radii of both , find the length of segment formed by joining the endpoints of the sector.

$AOB$ is a sector of a circle with center $ O$ and radius $OA = 10$. Circle with radius $3$ is inscribed in this sector such that it touches radius $OA$, radius $OB$ and arc $AB$. Find the length of ...
1
vote
2answers
48 views

Three sides of a $\triangle$ are known. If a circle with it's center on base of $\triangle$ touches the other two sides , find the radius of circle.

In $\triangle ABC$, $AB = 10, AC = 12$ and $BC = 18$. A circle is drawn such that its center is on side $ BC$ and it touches lines $AC$ and $AB$. Find the radius of the circle. By pythagoras ...
2
votes
2answers
53 views

Surface Area of a Sphere

I'm having trouble with finding the surface area of a sphere, without using any calculus. What I thought, was that the surface area of a sphere is fundamentally an infinite number of rings, ...
1
vote
1answer
43 views

Identify the locus.

Let $A,B,C$ lie on a straight line. $B$ is lying between $A$ and $C$. Consider all circles passing through $B$ and $C$. The point of contact of the tangents from $A$ to these circles lies on ..... We ...
2
votes
1answer
33 views

Inside a sector of a big circle , there are two touching circles. Find the radius of one of them.

Consider sector of a circle $OAB$. Circle with center $ M $ touches $OA$ at $P$, $OB$ a $Q$ and arc $AB$ at $N$. Circle with center at $L$ touches $OA$ at $C$, $OB$ at $D$ and circle with center $M$ ...
2
votes
1answer
171 views

Finding a curve which satisfies a special condition about angle

We can see that the angle of $$\frac{x^2}{a^2}+\frac{y^2}{1-a^2}=1\ \ \ (0\lt a\lt 1)$$ from every point on $$C : x^2+y^2=1$$ is $\pi/2$. $\hspace1in$ Then, here is my question. Question : If ...
0
votes
3answers
86 views

A circle is inscribed in sector of another bigger circle.Given A(circle) find the A(triangle formed by the center and the endpoints of the sector).

Consider sector of circle $MAB$. $∠AMB = 120◦$. A circle $S$ touches side $AM$, side $MB$ and arc $AB$ as shown in the figure. Area of circle $S$ is $75π/(7 + 4√3)$ . Find $4√3$ times the area of ...
0
votes
2answers
30 views

Geometry problem with 2 circles and a triangle

I tried to solve this problem: But I did not know how to do it so I looked at the answers and I saw E looked convincing because it is the only one that has square powers and D (from the diagram) is ...
1
vote
1answer
59 views

Simple Circle Problem

An elegant circle problem. It goes by many names. This is my version. Dog 1 is tied to a post by a leash 1 unit long. He shares half of his land with Dog 2 tied to a post 1 unit away from his own. ...
17
votes
3answers
280 views

What is the largest circle that fits in $\sin(x)?$

Imagine dropping a circle into the trough of $\sin(x)$. Would it reach the bottom or get wedged between two points on the curve? Depends on the size of the circle. So, what is the radius of the ...
1
vote
2answers
80 views

Three circles with two common points

Let $ABC$ be a triangle of any type and $A_1,B_1,C_1$ the feet of the heights. Denote $M,N,P$ the orthogonal projections of the point $A$ onto the lines $B_1C_1,C_1A_1$ and $A_1B_1$. The circes ...
0
votes
1answer
67 views

How to find the circumcircle radius from this following regular hexagon?

Given a regular hexagon $ABCDEF$. We draw diagonals $AC$ and $CE$. Then, we choose two random points inside the hexagon, call that $M$ and $N$, such that: $\frac{AM}{AC} =\frac{CN}{CE}$. If $B, M$ ...
0
votes
1answer
57 views

Determine the radius of the circle knowing that…

I have such a problem: determine the radius of a circle in which you know that two chords of lengths $9$ and $17$ intersect in a point, and that the distance between the middle points of these chords ...
2
votes
2answers
63 views

Why does the “T=0” method to calculate tangent work?

Given a random equation of a curve: $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$. Suppose we need to find the tangent to this curve at any point $A(x_1, y_1)$. A method given to me by my professor was the ...
1
vote
0answers
18 views

Grid overlay on an annulus. Move n squares to create a sector that is closest to the area of the original.

I want to create an image in photoshop, and need to break an annulus, pictured below, into smaller segments. I can use other methods to find the solution, but I'm interested to see how mathematicians ...
1
vote
0answers
30 views

Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
1
vote
1answer
37 views

Crossing Circles

On a plane, you are only allowed to draw circles. After drawing 1 circle, can you ALWAYS draw another so that the new circle crosses all existing circles at 2 points? Why?
0
votes
1answer
44 views

Inner tangent between two circles formula

As a programmer I need to draw the inner tangents between two circles, but only the segments, not the whole line. But the internet is surprisingly hostile to lazy programmers who don't know their ...
0
votes
1answer
63 views

If the arc length and chord length between two points in a circle are known , find radius of the circle?

If the arc length and chord length between two points (two points on a circle that constitute a minor arc ) in a circle are known , find radius of the circle?
4
votes
1answer
114 views

Length of median extended to the circumcircle

A triangle has side length $13,14,15$, and its circumcircle is constructed. The median is then drawn with its base having a length of $14$, and is extended to the circle. Find its length.
3
votes
1answer
62 views

Algebraic Proof that a Disk is Convex

After searching on Google for a while, I cannot seem to find an algebraic proof that a disk is a convex set. Intuitively, this seems obvious: if you take any two points $x, y$ in a disk, then the line ...
0
votes
1answer
42 views

Points of intersection of a line with two circles

I have the following representation: - line pass through the centers of the circles I have to find the coordinates of the points of intersection of the line with circles (4 points). From these 4 ...
1
vote
1answer
38 views

Tangents to a circle

For this construction, how would you show that the perimeter of the triangle $CDF$ is equal to $2BC$? Please include steps and whatnot.
2
votes
1answer
103 views

Equation for concentric circles?

I want an equation for concentric circles. In following image I am trying to draw concentric circles in Java but as you can see these are messed up. This is because their (x,y) coordinates (i.e. ...
0
votes
1answer
29 views

How to find the coordination of a tangent point on a circle?

I have a circle with the radius R, and coordinates of point A outside of the circle, and the coordinates of the center of the circle. I need to find the exact touching point of the tangent from point ...
2
votes
2answers
48 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
4
votes
1answer
44 views

Does an infinite collection of circles accumulates at a circle?

There is an infinite collection of closed circles in the plane, all within a finite bounding square. Does it contain an infinite sequence of circles that converge to a circle? Assume that a point is ...
0
votes
0answers
50 views

Calculate the radius of the circle - given the following in the figure

[HOMEWORK]Below is the figure in which the radius has to be calculated - and the answer has been provided, without the steps involved. After struggling for an hour or so, I'm not able to go ...
0
votes
3answers
57 views

How to check whether a line exists inside a circle or not?

I have a line equation in the form of ax + by +c = 0. And I have a circle with radius r. I want to know whether the line exists inside the circle or not??
1
vote
1answer
101 views

hyperbolic geometry (and circle ) construction problem

Was thinking about hyperbolic geometry, the Poincare Disk Model and Sweikarts constant and combined them all in a construction puzzle that I was unable to solve. My construction puzzle: Given: A ...
2
votes
0answers
108 views

Rounding Corners: How to calculate Fillet radius?

How do I find the maximum rounding I can apply to either corner for any amount of rounding on the other corner? The all circles are perfect circles, but I can't figure out the max size of the ...
1
vote
1answer
35 views

Geometrically prove that for a point on a diameter…

Geometrically prove that for a point on a diameter between the center point and the perimeter of a circle, the distance between this non-center point is the shortest distance to the perimeter. So $A$ ...
0
votes
1answer
52 views

prove angle between tangents and angle subtended by radii is suplementary

USING THE RESULT THAT THE LENGTH OF THE TANGENTS DRAW FROM AN EXTERNAL POINT TO A CIRCLE ARE EQUAL, prove that the angle between the two tangents drawn from an external point to a circle is ...
0
votes
1answer
22 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 ...
0
votes
1answer
43 views

Linear distance is proportional to angular distance, why?

Im my Fourier series book, the following is stated: We may specify the position of a point on the circle by its angular coordinate $\theta$, measured from some fixed base point. Since linear distance ...
2
votes
1answer
95 views

Two circles touch internally

Hello I've bean practicing for competition in math and can't seem to solve this problem,tried drawing chords,tangents,finding equal triangles,but couldn't seem to solve it.Any help would be ...
1
vote
1answer
44 views

Prove $\Delta APB $ is equilateral triangle

From a point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. If $OP$ is equal to the diameter of the circle, show that $\Delta APB $ is equiltateral. So this is the figure: I ...
2
votes
1answer
124 views

Numerical integration of a region bounded by an ellipse and a circle

Consider an ellipse (say with major axis $a$ and minor axis $b$) centered at origin with a concentric circle of radius $R$. Area of the region between the circle and the ellipse is $$A = \pi R^2 ...
2
votes
1answer
44 views

How to minimally move circles so that they don't overlap?

You're given a set of circles, all the same radius, residing at different locations in a 2d space. Some circles are in fixed positions. How do you make sure none of them overlap, minimizing the ...
1
vote
1answer
27 views

Given 3 points and there distances from eachother find a fourth point equidistant to the 3.

This question can also be asked: given a triangle, and its dimensions, whose vertices lie on the edge of a circle find the radius of the circle. I am not actually sure if there is enough information ...
1
vote
1answer
81 views

Finding the radius, distance of the center of circle inscribed in the square

I am trying to solve this question but can't figure out the last part. I was able to get answers for part A and B but i don't know how to approach/solve part C. Any help will be appreciated. The ...
10
votes
1answer
319 views

Thinking outside of the box

You want to draw a circle with a 4 inch radius. A trivial task for you and your trusty compass. When you go to grab your compass which has not had much love for a while you find it is rusted shut; ...
1
vote
1answer
58 views

Radian and the length of a chord of a circle

Question In a circle of radius $r$, an arc of it is $2S$ long. Find the length of the chord corresponding to that arc (AB in the diagram below) . Details I got this question in a math test. And ...