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

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12
votes
2answers
2k views

Proving collinear points

This problem is so hard that I cannot figure it out. I hope you guys can give me a small push on how to tackle this problem, as I have been thinking about this for, like a week. Here's the problem: ...
12
votes
1answer
565 views

How does one calculate the product of $\tan 1^{\circ} … \tan 45^{\circ}?$

I have seen a question asked on yahoo asking to find the value of $\tan 1^{\circ} \cdot \tan 2^{\circ} \cdot \dots \cdot \tan 45^{\circ}$ (in degrees) I have seen various results concerning ...
0
votes
2answers
244 views

Explain 2D ellipse function in terms of Circ

Suppose we have a two dimensional continuous linear shift invariant system has impulse response: $h(x,y)=\left\{ \begin{array}{ll} \frac{1}{2\pi a^2 b^2}, & \mbox{if } ...
1
vote
2answers
115 views

How do I calculate a point on each of three circles that have specific distance to each other?

I am trying to write code for a computer simulator. I need to simulate a complex mechanism where each link has a known length and the ends of the links are connected to a triangle. I would like help ...
-4
votes
3answers
3k views

Geometric Definitions: What is a straight line? What is a circle?

What is a straight line? I need a geometric definition of it. The equation of a straight line is known to me.I am saying about a straight line of 2D plane. What is a circle? I need a geometric ...
2
votes
1answer
4k views

Calculating circle radius from two points on circumference (for game movement)

I'm designing a game where objects have to move along a series of waypoints. The object has a speed and a maximum turn rate. When moving between points p1 and p2 it will move in a circular curve ...
13
votes
10answers
4k views

Finding circumference without using $\pi$

If the area of a circle is $254.34\ldots\text{ cm}^2$ it has a diameter of $18\text{ cm}$, is it possible to find the circumference without using or making the irrational constant Pi ...
5
votes
1answer
3k views

How to calculate a point on a circle knowing the radius and center point

I have a complicated problem and it involves an understanding of Maths I'm not confident with. Some slight context may help. I'm building a 3D train simulator for children and it will run in the ...
0
votes
2answers
174 views

Finding the locus of a point

I was thinking about the above problem .Can someone point me in the right direction? Thanks in advance for your time.
5
votes
1answer
868 views

Ноw many equal circles can be placed around a circle?

How many circles of radius $r$ can be placed around a circle of radius $R$ (close to it)? $r$ can be bigger, equal or smaller than $R$.
3
votes
1answer
424 views

Finding a circle that touch two other circles and a line

Given two circles $(x1, y1, r1), (x2, y2, r2)$ and a line passing through two points $A(xa, ya)$ and $B(xb, yb)$. How to find a circle $(x3, y3, r3)$ that is tangent to line and two given circles? I ...
5
votes
1answer
5k views

How to find an end point of an arc given another end point, radius, and arc direction?

Given an arbitrary arc, where you know the following values: end point (x1,y1), radius (r) and arc direction (e.g. clockwise or counterclockwise from start to end), how can I calculate the other ...
1
vote
1answer
788 views

find a circle tangent to an ellipse

As shown in the figure, the circle is moving upwards along the line $x=x_0$ http://i.imgur.com/bEntX.png suppose we know the following parameters: $a,b,x_0,r$ The ellipse equation is ...
2
votes
0answers
274 views

Drawing a Great Circle between two given points on Earth

I need to draw a great circle arc between two latitude and longitude points. For sake of example we will use the coordinates for LAX and JFK. JFK is 40.64°N / 73.78°W LAX is 33.94°N / 118.41°W ...
3
votes
1answer
87 views

Check If a point on a circle is left or right of a point

What is the best way to determine if a point on a circle is to the left or to the right of another point on that same circle?
1
vote
2answers
638 views

How to divide a circle into 9 rings / 1 inner circle with the same area?

The objective is to divide a circle of any size into 10 equal areas where 1 is a smaller inner circle and 9 are rings.
0
votes
0answers
302 views

Maximum latitude of a great circle

1 - I am trying to figure out the longitude at which a geodetic great circle reaches its apex. (I have a point and the azimuth at that point identifying the circle) I have found a good resource that ...
10
votes
3answers
4k views

What is the probability that the center of the circle is contained within the triangle?

Consider the triangle formed by randomly distributing three points on a circle. What is the probability of the center of the circle be contained within the triangle?
0
votes
1answer
232 views

equation for the region inside a circle

What equation or group of equations fill the entire or part of a region inside a circle without using inequalities? Update I don't know if this problem is already solved, I'm trying to find the ...
3
votes
3answers
25k views

X and Y coordinates of circle giving a center, radius and angle

I have to find the necessary translations in X and Y to move a point 0n a circle to another one. I have a center (X and Y coordinates), a radius, and a current position in radians. And given a value ...
4
votes
1answer
617 views

Geometric argument as to why the cyclic quadrilateral has the maximal area

I am looking for a purely geometric/intuitive argument as to why the cyclic quadrilateral has the maximal area among all quadrilaterals having the same side lengths. I am aware of couple of proofs, ...
1
vote
0answers
519 views

Finding tangent points of circle inside a triangle

Hi, This is really a part 2 of a previous questions of finding intersecting points of a circle and triangle. I'd like to run my approach by you all to see if I'm thinking correctly. Maybe there's a ...
3
votes
1answer
166 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
385 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
353 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
117 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
2k 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 ...
2
votes
3answers
550 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 $=(x_1, y_1)$ and Point 2 $=(x_2, y_2)$. I'd like to draw a circle around ...
0
votes
2answers
356 views

Circle and a quadrilateral

Q: The polygon circumscribes the circle. Find the perimeter.
1
vote
1answer
205 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
9k 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 ...
13
votes
8answers
31k 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?
1
vote
1answer
432 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
370 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
509 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
429 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
302 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
209 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
269 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
9k 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
132 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
897 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
208 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
6k 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
351 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 ...