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

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1answer
118 views

A circle touches the parabola $y^2=4ax$ at P. It also passes through the focus S of the parabola and int…

Problem : A circle touches the parabola $y^2=4ax$ at P. It also passes through the focus S of the parabola and intersects its axis at Q. If angle SPQ is $\frac{\pi}{2}$ find the equation of the ...
0
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1answer
24 views

Using an offset data point with x, y coords to find the true centre of a circle

I have a data point at (0, 0) where measurements of a tank's shell are taken from. I have used this data point to plot the circle in a graph. However, this data point is not the true centre of the ...
2
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4answers
235 views

Area of the intersection of four circles of equal radius [duplicate]

This picture basically shows a rearrangement of four quarters of a circle of radius 1. It asks for the shaded area. I got the answer to be $\frac{2\pi + 6}{13}$. But then it is incorrect. The way ...
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1answer
45 views

Average rate of speed relative to a given point

For this question I am mainly concerned about points A and B on the image below and the image below hopefully helps illustrate my question. If point B is fixed and A has to move in a strait line in ...
1
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1answer
59 views

Circular variation with repetition

I would like to know formula for circular variation with repetition. What I mean is : You have round table with n-spots. On every spot there can be number from 1 to k. So for n = 4 and k = 3 ...
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1answer
38 views

find the area of value of b in the equilateral

A circle meets the sides of an equilateral triangle ABC at six points D, E, F ,G, H , I in the figure . If AE= 4 ED = 26 , FG = 14 , and the circle with diameter HI has area πb, find b. sorry i ...
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1answer
25 views

In the circle below , mA= 86, mBDC= 32, mAD= 48 find the mBC, mCD

In the circle below, m∠A=86, m∠BDC=32, and mA͡D= 48 find mB͡C, mC͡D, mA͡B, m∠ADB, m∠ABD, m∠DBC, m∠BCD
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1answer
24 views

Finding the number of Circle or Circles in a Circle

Let a circle $A$ which radius is $10 m$ and another circle is $B$ which radius is $0.2 m$.Is it possible to say that what is the maximum number of circles $B$ can be drawn in circle $A$? I tried much ...
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2answers
54 views

High-School level question concerning circle and arcs

This question somehow is unsolvable to me. Any idead/hints wil be much appreciated. $AB$ is a chord which is cut ny the chords $CD$ and $EC$ in the circle. Givens: $\frown{AC} ...
3
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1answer
20 views

No four points with pairwise distance 1 can be contained inside a halfdisk of radius 1.

An open disk $D$ of radius $1$ in the Euclidean plane is the set of points with distance less than $1$ to the center of the disk. An open half disk $H$ of radius $1$ is obtained by "cutting" $D$ ...
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2answers
29 views

Proving a trigonometric relation using circle properties

Hi, I've been having trouble with this question, and would really like some help. What I've done so far is applied the cosine rule in the triangle PQR to find that $PR^2=a^2+c^2+2ac\cos\theta$. ...
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3answers
79 views

Write the equation of the tangent line of a circle

I'm totally lost with this question. I appreciate any kind of help. if the equation of a circle is $(x-3)^2+y^2=9$ Find : -Equation of the tangent line at $(2,2\sqrt2)$ -Equation of the tangent ...
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3answers
699 views

What does the Circle really mean?

Which of the following figure is really the circle? If a point is on the circle it means that point should be on the circumference is it? (point $Z$ on figure 1). Point $P$ on figure $1$ is inside ...
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1answer
29 views

Radius of circumscribed circle of triangle as function of the sides

Given the length ot the sides $a , b$ and $c$ of $ \triangle ABC$. What is the length of the radius of the circumcribed circle? After some formula substitution I came to the monster formula: $$ ...
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0answers
54 views

Proof: At most 3 circles of radius 1/2 fit into the interior of a halfcircle of radius 1

It is a well known fact that at most 7 interior disjoint circles of radius 1/2 can be centered in a circle of radius 1; note that they don't need to be fully contained in the radius 1 circle. I am ...
2
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1answer
52 views

I got stucked in middle of the problem. How to find the value of radius 'x' cm from the given figure?

![enter image description here][2] Firstly, i calculated the area of sector AOB by applying \frac 12 x (1.2 radians) x 20^{2} (formula for area of sector of circle) and calculated area of sector ...
3
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2answers
130 views

Geometry question: ray paths and circles

I was working on a problem and used the image below to make an argument regarding an effective line-of-sight (from one of my papers). My question below is more of an intellectual curiosity since the ...
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1answer
29 views

Prove that $\angle BAC + \angle OAP = 180^\circ$

Prove that if you construct two circle centered at O and P and intersecting at A with tangent lines BA and CA. Prove that $\angle BAC + \angle OAP = 180^\circ$. I'm having trouble just starting the ...
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1answer
117 views

Determine Circle of Intersection of Plane and Sphere

How can the equation of a circle be determined from the equations of a sphere and a plane which intersect to form the circle? At a minimum, how can the radius and center of the circle be determined? ...
5
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1answer
106 views

How many circles with radius $r_1$ can be inscribed in circle with radius $r_2$

Is there formula for finding the number of inscribed circles in a bigger circle? For example: Little circles radius: $7 cm$; Big circle radius: $50cm$;
3
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5answers
324 views

Coordinates of the point on the circle inscribed in a square

I try to find a way to calculate coordinates of a point nested on a circle inscribed in a square. The available variables, are: 1) side length of the square = 100; 2) circle radius = 50; 3) angle (a) ...
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0answers
94 views

Pre calculus Unit Circle

Suppose that you did not have the Unit Circle on Circle A, but rather a circle of radius $5$. Will the angle measures in degrees and/or radians change? Why or why not? Suppose that you did not have ...
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1answer
64 views

Area of similar triangle

Suppose that we are given a triangle whose area is known. put a circle C of radius r inside that triangle. How can we find the area of a triangle similar to the first one and whose inscribed circle is ...
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2answers
42 views

Length of tangent line segment to 2 circles

https://drive.google.com/file/d/0B-4lJHUDH1P5UEZ4QzNYcTNYQWs/edit?usp=sharing The image of the problem can be accessed in the above website. Two semicircles are tangent to each other. The ...
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0answers
37 views

Count balls to put in triangle

Given balls of radius $R$ we need to find how many balls can be put into a triangular container with sides $a,b$ and $c$. Example : Let $R=1$ and $a=3,b=4$ and $c=5$ then answer is $1$, as only one ...
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1answer
38 views

Area of shape made from quarter arcs of circles

I have this task. I would first calculate the square that I marked red. That's $6\times 6=36$. Then I add one circle with area $(1.5)^2\times \pi$. So the answer is E, because the area is $36 + 2.25 ...
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2answers
123 views

How to maximize area of two circles inside a rectangle without overlapping?

Two circles have to be drawn inside a rectangle of dimensions $W\times H$ such that the area of both circles is to be as large as possible without overlapping. Let the radii of the circles be $r_1$ ...
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1answer
41 views

equation for the radius of a circle that is tangent to two lines and passing through a specific point on one of the lines?

I'm interested in finding the equation for the radius (and optionally the center point) for a circle that is tangent to two lines and passing through a specific point on one of the lines. So far, I've ...
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0answers
29 views

Position n circles in circular layout

Given an index from 1 ... n, and a fixed width and height of each circle (and a fixed spacing), how would I calculate the center x coordinate and center y coordinate of each node to match the ...
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0answers
134 views

Significance of Orthocenter in real life

I have found that the circumcenter, incenter, and centroid have some connection with real life, for example centroid is used to find the center of mass of a 2d object.. however I am unable to find the ...
2
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1answer
33 views

Find the equation of line and finding a point in given example

The outer circle is $x^2+y^2=1$ and the smaller circle is $x^2+(y+1-r)^2=r^2$. The arclength is parameterised anticlockwise with $s=0$ at the bottom as shown. If we know $s_n$ and $s_{n+1}$ can we ...
0
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1answer
40 views

Number of integer lattice points within a circle

I am trying to solve a problem on codeforces, to be precised, this problem. I was able to figure out that the solution is $N(n) - N(n-1)$ where $N(n)$ is the number of lattice points withing a circle ...
2
votes
1answer
116 views

Pdf for distance between two uniform random points in a circle

This is my first post in the group and I would be very thankful for any help. I am trying to develop a probability distribution for a performance analysis in my thesis. I am trying to look in to ...
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1answer
65 views

Can $\pi$ and the $\pi$ in radians simplify?

I saw in a proof for the limit $$\lim_{x\rightarrow 0}\frac{\sin(x)}{x}=1$$ that, in one of the steps, you had to take the area of a section of a circle, in which you had to do $\frac{\pi r^2 ...
3
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1answer
52 views

Longest chord inside the intersection area of three circles

I am currently working on my masters thesis in computer science and I stumbled onto a geometry problem. My goal is to compute the length of the longest possible chord inside the intersection area of ...
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1answer
157 views

Calculus Riemann sums for circle and ellipse

I ran into this problem today. I need to compare the Riemann sums for a circle and an ellipse. I have no idea as where to start. Here's the question:
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1answer
137 views

Geometry Find the Radius of a circumcircle given the area of the triangle

Ok so here is what I know, the circumcircle of an equilateral triangle with an area of $4\sqrt{3}$ is drawn, calculate the radius lenght of the circumcircle. I also know that to find the radius I ...
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1answer
41 views

If$ x^2 + y^2 + Ax + By + C = 0 .$ Find the condition on $A, B$ and $C$ such that this represents the equation of a circle.

Also find the center and radius of the circle Here's my solution, I'm not sure if it's correct or not (specifically the conditions on $A$, $B$ and $C$. I feel that my conditioning is invalid and that ...
0
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2answers
42 views

Circle equations

Given that the circle C has center $(a,b)$ where $a$ and $b$ are positive constants and that C touches the $x$-axis and that the line $y=x$ is a tangent to C show that $a = (1 + \sqrt{2})b$
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2answers
68 views

equation of circle tangent to line with radius

Find the equation of a circle tangent to line $3x + y - 2 = 0$ at $(-1,5)$ and with radius $\sqrt{10}$. I've no idea on how to do this.
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1answer
45 views

Circle pass through 2 ponts with radius

Find the equation of a circle pass through (4,-3) and (-3,-4) with radius 5! I tried putting the x and y to equation(x-h)^2 + (y-k)^2 = r^2 then I don't know how to continue
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3answers
51 views

In what sense is a function on a circle the same as a $2 \pi$ periodic function on $\mathbb{R}$?

I was reading the appendix of Elias M Stein's Fourier Analysis and before proving the approximation lemma the author mentions the following Recall that a function on a circle is the same as a $2 ...
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1answer
78 views

General solution for intersection of line and circle

If the equation for a circle is $|c-x|^2 = r^2$ and the equation for the line is $n \cdot x=d $, and assuming that the circle and line intersect in two points, how can I find these points? Also as ...
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1answer
24 views

determine shortest distance between circle intersections

I have three circles positioned shown in the fig. Each of them has the same radius. I know the distance between each of them (A-B, B-C, A-C). My goal is to find the shortest path between B and C. The ...
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1answer
84 views

max points in circle given radius and min spacing between points

I want to know how many points (n) can be placed in a circle of radius r, with a minimum spacing s between points. I find postings for several similar problems -- smallest circle around a set of ...
0
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1answer
32 views

A,B,P are three points on a circle having centre O. If angle OAP=25 and angle OBP=35 , then the measure of angle AOB is???

A,B,P are three points on a circle having centre O. If angle OAP=25 and angle OBP=35 , then the measure of angle AOB is???
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3answers
40 views

Calculate the circumference of a circular lake

A lake has a diameter of $7$m and needs to be fenced for the protection for children. What length of fencing is required? Fencing comes in $1$m lengths, how many lengths are needed? What is the ...
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1answer
91 views

Finding equation of tangent of a circle that intersects the origin?

Given: circle with equation $(x-2)^2+(y-1)^2=4$. How to find equation of tangent line to the circle that intersects the origin? I easily found out that one of the tangents is $x=0$.
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1answer
49 views

Prove that the triangle areas are proportional to the radii

The line $MN$ is the radical axis I created. Because of its properties, we have $EM=MF, HN=NG, IQ=QL$, and it is perpendicular to $AC$. Everything is as you see on the diagram below. Here $(ABC)$ ...
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0answers
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What is the 'optimal' equal-area partition of a circle?

What is the (an?) n-partition of a circle that meets the following criteria: The boundaries of each partition can be represented as a union of finitely many finite-piecewise-smooth simple closed ...