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

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22
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5answers
1k views

Trying to understand why circle area is not $2 \pi r^2$

I understand the reasoning behind $\pi r^2$ for a circle area however I'd like to know what is wrong with the reasoning below: The area of a square is like a line, the height (one dimension, length) ...
2
votes
1answer
161 views

Drawing a circle tangent to a given circle and its origin is on y-axis

I am facing a problem and I do not know if it is solvable or not. Suppose I have 2 points and a distance, $P_1$, $P_2$ and $D_x$ respectively. I need a mathematical way to find the center of a ...
1
vote
1answer
215 views

Length bisection from circular arc

I am not sure if the following result is well known. I stumbled across it from the paper The Perimetric Bisection of Triangles by Dov Avishalom, where the result was stated without proof. I am ...
0
votes
1answer
111 views

Find the intersection between point and circle

given a line segment with endpoints P1 and P2 and a Circle with Center C and Radius R where it is known that P1 lies outside the circle and P2 lies inside the circle, what is an efficient way to find ...
2
votes
4answers
194 views

Quickest way to find a point on a circumference

Given the image below, A is the centre of the circle, B is a point on the circumference and AC and DB lie on parallel lines. Knowing A, C, D and the radius of the circumference, I need to find the ...
2
votes
1answer
246 views

calculated reflected point within circle

The problem to solve is this. Imagine a circle. We know two points on the circumference, anchor A and anchor B, they could be anywhere on the circumference of the circle. Draw a line between these ...
1
vote
1answer
151 views

Straightedge Only Construction of Tangents to Circle

Currently, there exists a question regarding straightedge only constructions; however, my specific question pertains something that is not found in that thread, and I do not think it will be answered ...
3
votes
1answer
176 views

What does Spivak want me to do?

This goes on in Chapter 8, on least upper bounds and related topics. I have proven $(a),(b),(c)$. The sketch is. $(a)$ If $\{a_n\}$ is a sequence of positive terms such that $$a_{n+1}\leq a_n/2$$ ...
0
votes
2answers
55 views

Problem with a circumference

I have the following equation for a circumference: $$9 X^2 + 25 Y^2 - 36 X - 50 Y = 154.$$ So far I only used this general equation: $X^2 + Y^2 + A X + B Y + C = 0$, but now $X^2$ and $Y^2$ are not ...
-3
votes
9answers
282 views

Why is $y + x = 3$ not the same as $y^2 + x^2 = 9$

I know this is impossible, but why is the following not possible: $y + x = 3$ is the same as $y^2 + x^2 = 9$ They're meant to be equivalent.
0
votes
1answer
1k views

Find arc center from tangent lines and 'rounding value'

Simple and common question: I want to round two intersecting lines with arc, so I need to know its center point. I have defined: AP - first line BP - second line |PR| - rounding scalar value, so ...
1
vote
2answers
232 views

Calculating circumference from 2d coords

I'm trying to calculate the circumference of a circle given say three reference points from a 2d coordinates that would form an arc. The problem is the reference points may be slightly inaccurate so ...
1
vote
1answer
2k views

Find the center of circle given two tangent lines and two points

Probably simple to solve but I'm a bit stuck. I am given two lines that are tangent to a circle and the circle must go through $P_1$ (which is the end of Line 1) and $P_2$ (which is the end of Line ...
41
votes
4answers
3k views

Do circles divide the plane into more regions than lines?

In this post it is mentioned that $n$ straight lines can divide the plane into a maximum number of $(n^{2}+n+2)/2$ different regions. What happens if we use circles instead of lines? That is, what ...
2
votes
1answer
156 views

How to constrain disks that intersection of them is inside unit circle

I have two disks $(x-a_1)^2+(y-b_1)^2\leq r_1^2$ and $(x-a_2)^2+(y-b_2)^2\leq r_2^2$, where $a_1$, $b_1$, $r_1$, $a_2$, $b_2$, $r_2$ are all known. What kind of constraint can I put on $a_i$, $b_i$ ...
1
vote
1answer
340 views

A question about circle geometry

Three points $A$, $B$ and $C$ are on a circle, $G$. Suppose $\overline{AB}>\overline{AC}$. Let $M$ be the midpoint of the arc of the circle containing the points A and N the point in $AB$ such ...
0
votes
2answers
83 views

How do I get get x and y position of a particular location on two intersecting circles (Vesica Pisces)?

I have the radius and center $(x,y)$ on both circles, but how do I get the $(x,y)$ of the red circle, or in other words how do I get the $(x,y)$ position of where the circles intersect at the top or ...
0
votes
1answer
94 views

Minimal rotation to avoid collision of circles

The discriminant of a certain quadratic equation which determines when two circles (hyperspheres?) will collide, provided they travel with a constant velocity is $$(\Delta v\cdot\Delta s)^2-(\Delta ...
0
votes
1answer
172 views

Geometry for Middle for schoolers (joining 5 points on a circle)

If there are five points on a circle. How many line segments can be drawn on it, but without overlapping the regions?
0
votes
2answers
1k views

2 concentric circles, inner circle has a tangent, relations between those points

AB is tangent to the inner circle, consider the trigonometric circle. Knowing the radius of both circles, is there a relation between those 2 point's coordinates ? Their coordinate being $A = (R ...
26
votes
12answers
27k views

Calculus proof for the area of a circle

I was looking for proofs using Calculus for the area of a circle and come across this one $$\int 2 \pi r \, dr = 2\pi \frac {r^2}{2} = \pi r^2$$ and it struck me as being particularly easy. The only ...
0
votes
1answer
148 views

Making a logo with processing, can't figure out a coordinate…

I'm struggling to make a simple logo, I have no deep knowledge of Inkscape so I'm doing it with a little bit of processing. The problem is I can't figure out how to determine one certain point's ...
1
vote
3answers
1k views

Difference Between Degrees on a circle

What kind of math would I use to calculate the difference between two degrees on a circle? Say, 38 and 272 degrees? When I just subtract one position from another sometimes it's more than 180 or ...
0
votes
2answers
5k views

How do you find an angle between two points on the edge of a circle?

I have a two points on the circle surface and I also know the center of the circle. I want to calculate the angle between those two points which are on the circle surface. Is this formula is suitable ...
18
votes
6answers
733 views

Is this 3D curve a circle?

The following is a curve in $3$ dimensions: $$\begin{eqnarray} x & = & \cos(\theta) \\ y & = & \cos(\theta - \pi/3) \\ z & = & \cos(\theta - 2\pi/3) \end{eqnarray}$$ Is the ...
2
votes
4answers
799 views

Extending the length of a curcumference by 1 meter

I once heard the following statement: Take a piece of string and measure the length around a ball. Now add 1 meter to the string and stretch it out evenly around the ball. Obviously the ...
3
votes
2answers
160 views

Savings when driving the inside edge of a curve.

I was wondering how many kilometers/meters I would save if I always drove on the inside edge of the curves between my home and workplace, compared to driving in the middle of the lane. If the lanes ...
0
votes
1answer
393 views

How to find the intersection of union of two circle groups

I have two groups of circles. S1 is the union of the first group and S2 is the union of the second group of circles. I know center and radius of all circles. I have to find the equation for the ...
1
vote
1answer
2k views

Calculate using cross-section of tunnel

http://imageshack.us/photo/my-images/545/88060057.png/ The figure shows the cross section of a railway tunnel. The radius of the tunnel is $3.5$m, i.e $OA = 3.5$m. $\angle AOB=90^\circ$. Calculate ...
1
vote
1answer
1k views

Find distance traveled by tips of hands of clocks?

The short and the long hands of a wall clock are $8$ cm and $12$ cm respectively. Find the sum of the distance traveled by their tips in $3$ days. Give your answer in terms of $\pi$. My ...
0
votes
1answer
514 views

Circular Sector to Circle Intersection

Is there a formula for determining if a sector intersects a circle (as well as determining if the circle/sector are inside each other)? Sector definition: A center point $P(x,y)$, a starting angle in ...
1
vote
1answer
182 views

A calculation involving two circles

I have two circles, one of which is completely within the other. They do not touch, but are not necessarily concentric. I am given the sum of their circumferences, and the difference in their areas ...
1
vote
1answer
612 views

Geometry Puzzle - Largest circle on Chess

The following puzzle was asked in company interview round.I have no idea ,how to do it? ...
1
vote
2answers
1k views

Formula for calculating the center of an arc

Is there a formula for calculating the point equidistant from the start point and end point of an arc given: 1) An arc is defined as: A center point $P$, a radius $r$ from the center, a starting ...
1
vote
2answers
385 views

A circle on the plane [duplicate]

Possible Duplicate: Parametric Equation of a Circle in 3D Space? I know that, for example, if a circle is on a plane with counter-clockwise orientation, and with center $(a,b)$ and radius ...
2
votes
3answers
76 views

From the given arc is known the start point the end point and a random point on the arc how we can find the center point coordinates?

From the given arc is known the start point the end point and a random point on the arc how we can find the center point coordinates?
0
votes
2answers
6k views

About Perimeter - Circumference of Quarter Circle

ASB is quarter circle. PQRS is a rectangle with side PQ=8 and PS=6 . What is length of ARC AQB ? Ans $5\pi$ Here is how I am solving it: Radius of Quarter circle = diagonal of ...
0
votes
1answer
828 views

Find the coordinates of a point on a circle given 2 points and an angle

I have a circle with A as a center, B and C 2 points on the circle. I have the coordinates of A (the center) and B (the point on the circle). How can I find the coordinates of C (another point on the ...
5
votes
2answers
1k views

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept

A circle is tangent to the $y$-axis at $y=3$ and has one $x$-intercept at $x=1$. Find the other $x$-intercept Like previously mentioned, I'm not all too familiar with circles. So, I plotted the ...
3
votes
4answers
2k views

Find center, radius and a tangent to $x^2+y^2+6x-4y+3=0$

For the circle $x^2+y^2+6x-4y+3=0$ find a) The center and radius b) The equation of the tangent line at the point $(-2,5)$ Now, I solved a) and got the equation $$(x+3)^2+(y-2)^2=10$$ with ...
0
votes
3answers
822 views

Triangle Inside Circle

If the radius of the circle is equal to the length of the chord $AB$, what is the value of $x$? How would I solve this problem ?
4
votes
1answer
271 views

Length of chord in circle - Which property

In the figure AB=4 , BC=6 , AC=5 and AD=6 what is length of DE ? Ans=9 I know there must be some property here that would solve this problem instantly but I cant figure it out any ...
1
vote
2answers
3k views

Area of Shaded Region

How would I calculate the area of the shaded region of a circle with radius 6 and length of chord AB is 6.
0
votes
1answer
245 views

clock related question

My question is- If the angle between the hour hand and the minute hand at 8 hours and x (>0) minutes is exactly 120 degrees then (11x - 200) equals? My solution is:40 I would like to know whether ...
0
votes
1answer
124 views

Radius by chordal length and segment area

Is there any formula to find radius of a circle segment if we know chordal legth and area of the segment?
0
votes
2answers
344 views

Calculating the points of tangency for two circles given a picture

I have two circles with the same radius and I want to calculate the points of tangency. For example, in the picture below, I want to calculate $(x_3, y_3)$ and $(x_4,y_4)$. I have the radius and the ...
0
votes
2answers
302 views

Solving a set of “circular” quadratic equations

$x_a'$ and $y_a'$ are unknown. What's the simplest way to solve it? Every time I tried, it grew into tremendous size or was unable to think out in reasonable amount of time due to it's complexity. ...
6
votes
1answer
509 views

Relationship between two centers of circles in a Venn diagram

Let $S$ be a circle of 1 unit area. No part of circles $A$ and $B$ are outside the circle $S$. Let $n(S)=1$, $n(A)$, and $n(B)$ be the area of circle $S$, $A$, and $B$, respectively. For the given ...
0
votes
3answers
1k views

Area of a sector - Inscribed Angle and Central Angle

I know the formula for the area of a sector of an arc made by central angle is $$\text{Area}_\text{Sector}= \frac{\text{Arc Angle} \times \text{Area of Circle} }{360}$$ Now my question is , Is this ...
3
votes
3answers
360 views

Deteriming an angle without Trig. ratios

I am trying to solve the current problem If O is the center of a circle with diameter 10 and the perimeter of AOB=16 then which is more x or 60 Now I know the triangle above is an ...