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

learn more… | top users | synonyms

3
votes
1answer
160 views

Finding intersecting points of a circle inside a triangle

If I have a triangle, and I wanted to place a circle with a given diameter that fits snuggly inside any one of the three angles, how can I find the x, y points of where the triangle and circle meet?
12
votes
2answers
375 views

Smallest inradius in a triangle

Inside triangle ABC there are three circles with radius $r_1$, $r_2$, and $r_3$ each of which is tangent to two sides of the triangle and to its incircle with radius r. All of $r$, $r_1$, $r_2$, and ...
2
votes
2answers
2k views

Is the tangent function (like in trig) and tangent lines the same?

So, a 45 degree angle in the unit circle has a tan value of 1. Does that mean the slope of a tangent line from that point is also 1? Or is something different entirely?
2
votes
4answers
140 views

How do I find the points of a circle?

Say you have a center of $(5, 5)$ and a radius of $2$. If you went for each x-value in $\{3, 4, 5, 6, 7\}$, how would you find the y value? EDIT: I have this code in C# ...
1
vote
2answers
339 views

Circle geometry: nonparallel tangent and secant problem

If secant and the tangent of a circle intersect at a point outside the circle then prove that the area of the rectangle formed by the two line segments corresponding to the secant is equal to the area ...
2
votes
2answers
111 views

Constrain Random Numbers to Inside a Circle

I am generating two random numbers to choose a point in a circle randomly. The circles radius is 3000 with origin at the center. I'm using -3000 to 3000 as my bounds for the random numbers. I'm trying ...
4
votes
2answers
1k views

Find if a point is in a circle

I am coding a video game, but I am not so good at the math. I am hoping for some help here: Given: $X, Y$ that is the center of the Circle $R$ that is the radius of the Circle $X_1, Y_1$ that may ...
1
vote
3answers
526 views

Equation to determine radius for a circle that should intersect a given point?

Simple question. I tried Google but I don't know what search keywords to use. I have two points on a 2d plane. Point 1 = x1 and y1, and Point 2 = x2 and y2. I'd like to draw a circle around Point ...
-1
votes
2answers
304 views

Circle and a quadrilateral

Q: The polygon circumscribes the circle. Find the perimeter.
1
vote
1answer
186 views

Finding the lengths of lines outside of a circle when they're not tangent

I recreated the question in paint above ^ The line is not tangent to the circle.
4
votes
1answer
8k views

Find the coordinates of a point on a circle

I have a circle like so Given a rotation θ and a radius r, how do I find the coordinate (x,y)? Keep in mind, this rotation could be anywhere between 0 and 360 degrees. For example, I have a ...
11
votes
5answers
28k views

How can I find the points at which two circles intersect?

Given the radius and $x,y$ coordinates of the center point of two circles how can I calculate their points of intersection if they have any?
0
votes
1answer
405 views

how to draw these circles?

How to draw these circles? I'm looking for a method which I can do it with Adobe Illustrator. (or draw in GeoGebra and export to illustrator) (Adapted from dribbble, created by Olaf Muller.)
0
votes
1answer
66 views

What function could describe this situation on a Cartesian plane?

I have a problem as follows - I have an arc, with a point on each end. And angle $a$ is how far the arc goes. I need to find the top right point ($P(w, x)$) in relation to the $r$, $P(x, y)$, and $a$ ...
0
votes
1answer
1k views

Generate random points on the perimeter of a circle

I have a circle of radius r and access to a random number generator. What is a method to generate random (x,y) values ...
1
vote
1answer
352 views

Equation of a circle with specific conditions

I am trying to find the equation for a circle that has the center at (-1 , 4) and passed through the point (3, -2) This seems like a straightforward problem. $$(x+1)^2+(y-4)^2 = 16$$ The radius ...
3
votes
1answer
453 views

How to get the diameter of multiple circles?

How can I get the length of the red line, if I got the diameters of all black circles? I'd prefer to get the lengths of the right example but I think it's much more difficult.
1
vote
1answer
386 views

Circular motion “calculate the angle”

I have a equation i need to find out how they hang together. angel = (velocity * time) - (acceleration * time * time / 2) I know circumference of a circle: ...
1
vote
0answers
287 views

Completelly cover area with minimum number of maxed circles NP-completeness (or harder) proof

everyone. I'm looking for paper with proof of NP-completeness following, or similar problem. Given: Area $S \subset \mathbb{N}^2$, let it be convex or rectangular, I believe it doesn't matter ...
1
vote
0answers
205 views

Area of ring section closed within a rectangle

I wish to find out the area of a section of a ring which can be acted on my a rectangle 100mm wide by 60mm height. I know the inner diameter,ID and outer diameter,OD of the ring and the width of the ...
1
vote
3answers
249 views

Prove that point M is on circle c

It's hard to create question names that make sense. Anyhow, the following is another question from my math assignment. Line-segment AB has a fixed length of 10 units. point A moves on the positive ...
1
vote
1answer
8k views

How to calculate radius when I know the tangent line length?

For my math homework, I was asked this question: The tangent lines from O hit a circle with center M and radius r in R and S. Calculate r. -The length of OR and OS is 4 How do I calculate the ...
1
vote
2answers
128 views

area of a circle - 3/4th

How to find the pixels of that line which is crossing the circle? Is there any formula? Iam getting the line's end points
2
votes
0answers
64 views

Circle, triangle and probability [duplicate]

Possible Duplicate: Probability distribution functions for the perimeter and space of triangle with fixed radius You choose three points (distributed uniformly) on the circle randomly. They ...
1
vote
1answer
794 views

Surface Area Problem with Specific Formulas

I noticed this question in a Math Problem-Set book. These were the only formulas allowed: $1. Area(quadrant) = \frac{1}{4}\pi r^2$ $2. Area(square) = (side)^2$$3.Area(semicircle) = \frac{1}{2} \pi ...
2
votes
3answers
192 views

How do I rearrange this formula? Circles around a larger circle.

My A-Level algebra is failing me. Can someone please tell me how to rearrange this formula to give $n$ when you know $R$ and $r$. $R \sin(180^\circ/n)/(1 - \sin(180^\circ/n)) = r$ This formula is ...
0
votes
3answers
5k views

How do I get the slope on a circle?

I have drawn a circle by doing this in Matlab: syms x; ezplot(cos(x),sin(x)) I get the tangent point at which I want my tangent to be by taking $x = \cos(3.1415)$, ...
7
votes
1answer
337 views

Cyclic Pentagon

Consider the above pentagon. Suppose that the distance from point $A$ to $BC$ is $a$, the distance from $A$ to $CD$ is $b$, and the distance from $A$ to $DE$ is $c$. In terms of this, how can we ...
3
votes
1answer
482 views

Area of triangle ABC inside circle

Consider the following diagram: $AB+AD=DE$, $\angle BAD= 60$, and $AE$ is $6$. How do we find the area of the triangle $ABC$?
1
vote
1answer
181 views

find distance from point in circle to perimiter

If I have the following circle, with centre in red and a random point in the circle in blue. I know the radius ,r, length of d, and the angle p: I then create a a new green point and I know the ...
6
votes
5answers
388 views

Prove this property for an arbitrary circle

Prove that in an arbitrary circle, the point on the circle closest to the origin must lie on the extended line connecting the circle's centre and the origin.
2
votes
1answer
101 views

What does 'the forward theorem' refer to?

I have seen the following in a circle geometry proof in a Cambridge textbook: We have proven that angles at the circumference standing on the same arc of a circle are equal. The converse of this ...
1
vote
2answers
210 views

How many coordinates are necessary to determine a sphere?

Do determine a circle, you would need at least three coordinates. How many are necessary to determine a sphere?
8
votes
3answers
25k views

How do I calculate the intersection(s) of a straight line and a circle?

The basic equation for a straight line is $y = mx + b$, where $b$ is the height of the line at $x = 0$ and $m$ is the gradient. The basic equation for a circle is $(x - c)^2 + (y - d)^2 = r^2$, where ...
0
votes
3answers
348 views

Do an axis-aligned rectangle and a circle overlap?

Given a circle of radius $r$ located at $(x_c, y_c)$ and a rectangle defined by the points $(x_l, y_l), (x_l+w, y_l+h)$ is there a way to determine whether the the two overlap? The square's edges are ...
1
vote
2answers
530 views

x Points around a circle

I would like to calculate x number of points around a circle using the circle's radius/diameter. For example, if I wanted 24 equidistant points around a circle with radius 30, how could I go about ...
0
votes
2answers
224 views

Diameter of circle with n points where adjacent points are m distance apart

How do I calculate the diameter of a circle that has n evenly-spaced points on its circumference where adjacent points are m distance apart?
0
votes
3answers
99 views

Calculate incircle radius.

A circle is inscribed in a right angled triangle ABC where AC is the hypotenuse. The circle touches AC at point P. Length of AP = 2unit and CP = 4 units. What is the radius of the circle?
3
votes
1answer
154 views

Bounds for the size of a circle with a fixed number of integer points

I know that there are infinitely many rational points on the (unit) circle. I am interested in the following question: How large has the radius of a circle to be, such that there are at least $n$ ...
2
votes
2answers
2k views

Equation of sine wave around a circle

Consider a sine wave having $4$ cycles wrapped around a circle of radius 1 unit (its center needs not be the origin of a Cartesian coordinate system). Assume that the length of axis of the sine wave ...
1
vote
1answer
556 views

Relationship between the sides of inscribed polygons

In my math textbook there's a demonstration for the calculus of the circumference of a circle that involves regular polygons inscribed in the circle, but I don't get it. The book gives the following ...
12
votes
1answer
854 views

A geometry problem seeking for proof

Circle $\odot O_1$ is tangent with circle $\odot O_2$ at $P$. Two tangent lines $AE$ and $AF$ of circle $\odot O_2$ meets circle $O_1$ at $B$, $G$ and $C$, $H$, respectively. $D$ is the in-center of ...
14
votes
6answers
747 views

Why do we use the Euclidean metric on $\mathbb{R}^2$?

On the train home, I thought I would try to prove $\pi$ is irrational. I needed a definition, so I used: $\pi$ is the area of the unit circle. But what is a circle? A circle is the set of tuples ...
22
votes
2answers
2k views

Divide circle into 9 pieces of equal area

I'd like to divide a unit circle disk into nine parts of equal area, using circle arcs as delimiting lines. The whole setup should be symmetric under the symmetry group of the square, i.e. 4 mirror ...
0
votes
2answers
576 views

Problem with finding the equations of the lines tangent to a certain circle

This is a long question, and might seem like a repost of my earlier questions, but it isn't, hear me out: In my book is written: The equation of the line tangent to the circle $x^2+y^2=r^2$ in the ...
0
votes
5answers
667 views

Find the equation of a circle which intersects another circle perpendicularly

'Find the equation of the circle with its center at $M(4,3)$ which intersects the circle $(x-3)^2+y^2=5$ perpendicularly' How can 2 circles have a perpendicular intersection, is this even possible? ...
0
votes
1answer
170 views

Put this equation of a circle in its standard form

$ x^2 + y^2 = 4x+4$ How to put it in the standard form: $(x-a)^2 + (y-b)^2 = r^2$
0
votes
1answer
132 views

Question about units and area of a circle?

Andrea is preparing an installation manual for a cell-phone tower to be used in a European country. The tower specifications are in imperial units, and she must convert them to SI for their client. ...
1
vote
1answer
302 views

dividing an offset circle into triangles

First of all - I am sorry if it is the wrong forum or if this is a very trivial question. I am not a mathematician nor a trigonometry genius - and therefor I would ask a simple answer that someone ...
0
votes
1answer
1k views

Find the equation of a circle given the radius and center (with vector length notation)

I want to find the equation but use vector length notation and I'm not sure about how to write it. $$ a) r = 2, A(-1; 1)$$ the line I'm not sure - $$|[x-x_0 , y-y_0]|^2 = r^2$$ then I do $$(x+1)^2 + ...