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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2
votes
2answers
332 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...
1
vote
2answers
86 views

Geometry: Arcs of a Circle

I think this is solved using the Pythagorean theorem but cant figure out how to get the length of PQ. Any help?
0
votes
1answer
19 views

Pont of contact tangent_Circle

The point of contact between a line $lx+my+n$ and the circle $x^2+y^2=a^2$ is $(-a^2l/n,-a^2m/n)$ What is the POC between the same line and the circle $x^2+y^2+2gx+2fy+c$?
1
vote
1answer
105 views

Smallest Circle that encircles $4$ circles

I want to calculate the radius of the smallest circle (radius $R$) that can hold $4$ circles (with radii $a, b, c, d$) inside it, such that: No circles overlaps one other. $a \ge b \ge c \ge d.$ ...
0
votes
1answer
113 views

Positioning Circles in a Ring

I am working on a program and need to be able to draw circles around the ring. The circle currently in the ring is manually placed. Is there an equation for drawing non overlapping circles inside a ...
6
votes
4answers
826 views

How to know location of a point?

I have a circle formed with three given points. How can i know whether another given point is inside the circle formed by previous three points. Is it determinant i need to calculate? Then what are ...
2
votes
2answers
1k views

How do I find the area of a circle inside a square?

In the figure above, the circle with center $O$ is inscribed in square $ABCD$. What is the area of the shaded portion of the circle? (A) $\pi/4$ (B) $\pi/2$ (C) $\pi$ (D) $3\pi/2$ (E) $2\pi$
2
votes
3answers
4k views

Get location of vector/circle intersection?

I'm a coding guru, and I'm good with math - but only math that I know. Which isn't even at calculus level yet. So I'm hoping I can get some help here for my algorithm. Say I have a circle. I know its ...
0
votes
2answers
559 views

Determine the coordinate of the point where line and circle collide/intersect - how to solve for x

I would like to determine the point $C$ in this image: (assume I have radius value). After the hours of research and refreshing some memories from school days, I've got: Please assume... Point: ...
0
votes
1answer
98 views

Space filling problem with equal radii on earth

I have two circles. Both origin at San francisco $(37.77493,-122.419415)$, The larger circle has Radius $R_1$, the smaller circle has radius of $R_2$. What's the fewest number of additional ...
0
votes
1answer
389 views

Analytical geometry - circles

How do you find the point for a circle and find the radius when $x^2$ has a co-efficient?
0
votes
1answer
76 views

Find angle in secant/chord diagram

What's the easiest way to show x=35 in this diagram? I eventually figured it out by drawing in two lines and chasing angles: However, this is a 10th grade question, so I'm sure there's an ...
2
votes
5answers
309 views

Arcs of a circle Geometry and angles

How do I find out what the radius length of the angle is? The answer is D by the way.
1
vote
2answers
317 views

How can i find the lenght of a side of a polygon with known number of sides that has a circle with known diameter inscribed in it?

How can i find the lenght of a side of a polygon with known number of sides that has a circle with known diameter inscribed in it? I'm a web-developer intereseted in this certain problem, that would ...
5
votes
2answers
217 views

Competition style problem circa 1992

We're given a triangle $ABC$. Going clockwise, let $B_1$ and $B_2$ be distinct points on the segment $AC$ ($B_1$ is between $A$ and $B_2$), let $A_1$ and $A_2$ be distinct points on the segment $CB$ ...
1
vote
3answers
84 views

Another complex analysis question

I am going to have an analysis exam soon and I found the following question in a past paper: Evaluate the integral counterclockwise $$\int |z| \overline{z} \, dz$$ where y is the closed curve ...
1
vote
1answer
105 views

Analysis Exam Questions

I am going to have an analysis exam soon and I found the following question in a past paper: Evaluate $$\int \frac{-y \, dx + x \, dy}{x^2+y^2}$$ a) Once counterclockwise around the circle $$x^2 + ...
0
votes
3answers
774 views

Find the length of this chord.

I've been trying to solve this geometry question for past 2 hours but haven't got the answer yet. There are two concentric circles or radius $8 cm $ and $13 cm$ with the common center $O$. $PQ$ is ...
1
vote
1answer
60 views

An arc of one-sixth of the circumference subtends a central angle of how many degrees?

How do I find the central angle with the following information: An arc of one-sixth of the circumference subtends a central angle of how many degrees? Do I just use the formula to find the angle even ...
2
votes
2answers
2k views

To find tangents to given circle from a point outside it

Find the combined equation of two tangents drawn from $P(x_1,y_1)$ to the circle $x^2+y^2 = a^2$. Point $P$ lies outside the circle.
0
votes
1answer
569 views

Given one endpoint on an arc of a circle and the radius and arc angle, how to calculate the other endpoint of the arc?

I have a circle with an arc beginning at point $(x,y)$. The radius is $r$, the arc angle(w/ respect to center) is $\theta$. How do I calculate the end point of the arc $(a,b)$ ? I know that the ...
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
561 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
240 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
113 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
2k 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
830 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
386 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
4k 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
766 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
270 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
86 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
625 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
296 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
225 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
24k 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
611 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
515 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
164 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
379 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
345 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
114 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 ...