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

learn more… | top users | synonyms

2
votes
1answer
491 views

Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something I'm struggling with for a project. :) Basically, there are two circles, represented ...
2
votes
1answer
122 views

Finding the incircle of a circle sector

I'm not great at mathematics so I'm sure this is trivial to most. I have been searching around however and not been able to find how to figure out the incircle of a circle sector, or, in other words, ...
0
votes
1answer
94 views

Tangents to Circle

Find the equation of the tangent at the point (acosØ,asinØ) on the circle x^2+y^2=a^2. Tangents are drawn from the point (2a,2a) to the above circle. If the coordinates of the point of contact be ...
1
vote
1answer
1k views

Radius of an arch given length and Area of sector

the lengh of an arc of a circle is 12cm.the corresponding sector area is 108cm^2 Find the radius of the circle.
3
votes
2answers
5k views

Calculating the coordinates of a point on a circles circumference from the radius, an origin and the arc between the points

We have a circle with the known radius $r$ and the circumference $2\pi r$, and we know a point $P_1$ somewhere on it's circumference. Now, we want to get the coordinates $[x_{P_2},y_{P_2}]$ of the ...
0
votes
3answers
87 views

Circle- basic question [closed]

I know this is a basic question, but if I have a circle with radius 2 and I look at the area on the circle between angles $-\pi$ and $\pi$, will that be the bottom half of the circle?
3
votes
2answers
164 views

Apollonius circle

I'm given two points, $A$ and $B$, and two lengths, $b$ and $c$. I need to find the locus of point $C$ such that $BC:AC=b:c$. This link describes Apollonius circle of first type, but I can't seem to ...
0
votes
3answers
132 views

How many circles fit in the same two dimensional orbit?

I'm trying to figure out how many circles/planets can fit in the same two dimensional orbit. All of the planets and orbits are perfect circles but the planets size and amount can vary. This is for ...
1
vote
1answer
102 views

Tangent to circle

The circle $x^2+y^2-4y+3=0$ passes through the points $(0,1),(-\frac{24}{25},\frac{43}{25}),(1,2)$. Its Centre is $(0,2)$ and its radius is $1$. I am asked to find the tangent to the circle through ...
0
votes
3answers
61 views

Why exactly is π(mean of radius)² less than the mean of the areas calculated for each radius?

For example, a uniformly distributed value for a radius between 0 and 1 is calculated many times and the area for each radius is calculated: ...
2
votes
4answers
591 views

Circle/Triangle math problem

The question asks to find angles $\angle X$ and $\angle Y$, however I don't know how to do this without assuming that lines $\overline {GO}$ and $\overline{OJ}$ are parallel. The only angle given is ...
1
vote
2answers
6k views

Calculating a circles radius from two known points on its circumference

For a simulation, I need to be able to calculate the radius $r$ of a circle $C$, knowing only two points on its circumference, $P_1$ and $P_2$, as well as the distance between them ($a$) and how much ...
12
votes
2answers
404 views

6 point lying on a common circle

$Z$ is an interior point of segment $XY$. Three semicircles are drawn over segments $XY$, $XZ$ and $ZY$ on the same side. The midpoints of the arcs are $M1$, $M2$ and $M3$ respectively. A circle ...
2
votes
1answer
3k views

How to find the central angle of a circle?

My book states the following: Likewise, we can take a circular cone with base radius $r$ and slant height $l$, cut it along the dashed line in Figure 2: and flatten it to form a sector ...
0
votes
1answer
49 views

How do you calculate the velocity of the pencil?

I'm drawing a quarter circle with a pencil on a sheet of graph paper. The radius is 10cm. At a given moment in time the velocity at which I am moving the pencil is 5cm/s (centimeters per second). I ...
1
vote
1answer
279 views

Calculate vector position

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions. Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...
0
votes
1answer
468 views

Formula to calculate a position given three 2D locations and distance

I am doing a project for my final year computer science and normally post on stack-overflow but this question seems more suited for here. I need a formula to calculate my position from three 2D points ...
1
vote
2answers
361 views

Bounding box enclosing circles, that complies with ratio constraints

Given a circle centered at $A$, with radius $R_a$ and another radius $R_b$, I need to find a center for circle $B$ such that both circles are tangential, and the bounding box including both circles ...
2
votes
2answers
326 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
104 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
106 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
811 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
3k 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
542 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
94 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
387 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
74 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
303 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
297 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
212 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
755 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
59 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
1k 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
549 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
1k 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
560 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
237 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
112 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
2answers
2k 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
3k 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
3k 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
173 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
787 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
362 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 ...