Tagged Questions

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
61 views

circular reasoning in proving $\frac{\sin x}x\to1,x\to0$

The classic proof for $\frac{\sin x}x\to1,x\to0$ is using a squeezing theorem based on arguments about areas of circles. But as far as I know, all deduction of formula of circles' area is based on ...
-4
votes
1answer
34 views

Help me with this question [on hold]

Length of AB, BC and CD are equal. length of AD=9,AE=6. DE is tangent to the circle. Find the length of CE Square (CE^2)
2
votes
1answer
13 views

Graphing Circles, Ellipses, Parabolas, and Hyperbolas

I need help plotting a curve on a graph where the distance from focus1 is always the same ratio to the distance from focus2. For instance, lets assume focus1 is -5 along the x axis, and focus2 is +5 ...
0
votes
1answer
29 views

Calculate distance in x,y from center based on distance and degrees.

I'm terribly sorry if this question is written like a 5-year old.. But that's the level I'm on in terms of math and coordinate calculations. (Just realized I don't even know what to tag this question ...
1
vote
1answer
45 views

Finding circle with two points on it and a tangent from one of the points

Two points P1(x1,y1) and P2(x2,y2) are known. In addition, a line slope passing through P1 is known. The aim is to construct a circle (or circular arc) that it passes through both P1 and P2 and it is ...
0
votes
1answer
63 views

Differentiation of a circle

As a discus thrower is spinning counterclockwise to throw a discus, the discus travels along the path given by the circle $x^2+y^2=4$. If the discus is released at the point $(\sqrt2,\sqrt2)$ and ...
-1
votes
0answers
29 views

Find the distance between circles centers [on hold]

We have equations of 2 circles. First: $x^2+y^2-2y-19=0$. Second: $x^2+y^2+2x-4y-1=0$. Needs to find the distance between circles centers.
0
votes
0answers
22 views

What is the sum of the interior angle of a circle?

There is a convenient formula for deriving the sum of the interior angle of polygons which is $$180^\circ\cdot (n-2)$$. By building the limit it seems that for a circle the value is infinite. But it ...
2
votes
1answer
18 views

In every polygon circumscribed about a circle, there exist three sides that can form a triangle.

How can one show that in every polygon circumscribed about a circle, there exist three sides that can form a triangle? (This was posted by another user and then deleted while I was typing my answer.) ...
0
votes
2answers
79 views

Number of ways to seat people around a circular table

I got (i) which is $9!$, but there are no answers for the second question. I stated that $$P(\text{none together})=1-P(\text{3 together})-P(\text{2 together})$$ and got the answer $7/12$. Is this ...
0
votes
0answers
22 views

find points on circle in 3D pace perpendicular to line

I'm working with 3D image data and have little algebraic knowledge. I have an 3D image whit each pixel divined by its x,y,z position. What I need is to get the values of all pixels on a circle inside ...
2
votes
5answers
247 views

How can I find the radius of a circle from a chord and a section of the radius?

Draw a circle with center O. Line AD is a chord that is 8cm long. The arc above is smaller than the one below. B is the center of AD. Line CB is a line that is 2cm long. It meets AD at 90°. ...
1
vote
1answer
22 views

Computing overlapping circle positions, equidistant from each other.

Hello, I am a programmer and I wanted to develop an application that would have several overlapping circles in the same location, where each circle can be selectable. Is there a mathematical way of ...
-2
votes
0answers
31 views

Area of a circle shall equal the area of a square [closed]

How can I, using bolzanos theorem, discuss the equal areas of a circle and a square? How can this be shown in a graph? Would be really grateful if any could help me! :)
3
votes
0answers
21 views

Find the minimum radius of the circle which is orthogonal to two given circles

Problem : Find the minimum radius of the circle which is orthogonal to both the circles $x^2+y^2-12x+35=0$ and $x^2+y^2+4x+3=0$ . Solution : Let the equations : $x^2+y^2-12x+35=0.....(i)$ and ...
0
votes
3answers
19 views

Cyclic quadrilaterals - finding the size of an angle

I know this might seem like a really simple question, but I really don't understand where I am going wrong. I am familiar with cyclic quadrilaterals as well as their properties, but this question ...
1
vote
3answers
15 views

Find the radii of the two circles which pass through the point $(16,2)$ and touch both axes

How can I find the radii of the two circles which pass through the point $(16,2)$ and touch both the axes? I've only ever seen demonstrations using three normal co-ordinates; or two normal ...
1
vote
2answers
22 views

If the length of tangent drawn from an external point P to the circle of radius $r$ is $l$ , then prove that area…

Problem : If the length of tangent drawn from an external point P to the circle of radius $r$ is $l$ , then prove that area of triangle form by pair of tangent and its chord of contact is ...
3
votes
1answer
52 views

Areas between intersecting chords

In the circle below let the two chords be called $C_1$ and $C_2$, and their intersection be some point that is not the center. The chord power theorem tell us that $a \cdot b = c \cdot d$. I am ...
0
votes
1answer
24 views

How to calculate point on circumference of circle given radius

I am trying to come up with a formula to calculate the y co-ordinate of the point on the circle in the attached picture (i.e. delta y) based on the circumference of the circle and the distance x. ...
1
vote
0answers
34 views

Inverse with respect to a given circle

Determine the inverse with respect to a given circle $g:\mathbb{R}^{2} \to \mathbb{R}^{+}, g(x,y)=x^{2}+y^{2}$. I have looked around for non geometric derivations without finding any of value. ...
1
vote
1answer
42 views

Find the maximum perpendicular height between a chord and an arc.

I am doing a maths modelling project, and I am stuck on a part. I have a (arc length) and L (chord length), but I want to find H, the maximum perpendicular distance between them! Any help would be ...
-2
votes
0answers
85 views

Circle geometry question. [duplicate]

I've been having trouble with this circle geometry question in my self-study beyond the course. I had stumbled across it an hour ago, but am not sure how to prove this. ...
0
votes
0answers
33 views

Area of a circle of Radius “r” in a rectangle

This is a very basic problem but i would like to ask as i am unable to resolve it. I have a rectangle of the following dimensions. $Length = L$ $Width = W$ I picked a point ($x,y$) in this ...
1
vote
1answer
19 views

Show that the common tangents to circles $x^2+y^2+2x=0$ and $x^2+y^2-6x=0$ …

Problem : Show that the common tangents to circles $x^2+y^2+2x=0$ and $x^2+y^2-6x=0$ form an equilateral triangle. Solution : Let $C_1 : x^2+y^2+2x=0$ here centre of the circle is $(-1,0) $ and ...
4
votes
4answers
84 views

Equation of a line tangent to circumference

Discover the general equation of the tangent line to the circumference $x^2 + y^2 - 2x + 4y + 1 = 0$ by the point $(3,4)$. NO CALCULUS. by the circumference equation i discovered that $C(1, ...
0
votes
0answers
33 views

Parametric Equation of a parabola from the derivative of the parametric equation of a circle

Find the velocity and trajectory to throw a ball from a Ferris Wheel to a friend standing below. The Ferris Wheel has a diameter of 16 meters and its highest point is 19 meters above the ground. It ...
0
votes
1answer
55 views

intersection of 4 circles

Hi I'm doing some programming challenges for fun and I am trying to work out the maths required to solve this problem. It has been 10 years since I did any maths in anger like this so i'm a bit ...
2
votes
1answer
47 views

Circle Equation Surjectivity

Consider the circular function $g:\mathbb{R}^{2} \to \mathbb{R}^{+}$, $g(x,y)=x^{2}+y^{2}$. Show that it is surjective and continuous. Note This post has been amended in accordance with the ...
0
votes
3answers
26 views

How to determine family of circles passing through two given points?

The question asks to show that the equation of any circle passing through two given points takes a certain form. I have obtained the points as being $(2,1)$ and $(2,-1)$ but I'm not sure as to how to ...
1
vote
1answer
35 views

power of a point (circles) questions.

Lets say we have two circles call them $O_{1}$ and $O_{2}$. Let $a_{1}$ and $a_{2}$ be the arcs of the circles. Then when it comes to two circles, three cases arise. They intersect at two points, they ...
1
vote
2answers
102 views

Show that four vertices of a square cannot lie on four concentric circles, radii of which form an arithmetic sequence

My teacher said it's solved using proof through contradiction. I've considered cases of the centre of the circle, but I lose geometry big time so not sure how to do this.
5
votes
1answer
131 views

Symmetrical of a triangle's vertexes

I have the following problem : Show that the symmetrical (ie reflection) of a triangle's vertexes by the opposite side are aligned iff the distance between the orthocenter and the circumcenter is ...
0
votes
1answer
12 views

Quadrilateral Inscribed angles calculation with one arc angle

I am trying desperately to solve following problem. How can I solve it, the image and question is included in image
0
votes
0answers
11 views

Estimating the mean Euclidean distance between two overlapping, not-matching shapes

I’d like to determine the mean distance between two irregular overlapped, not-matching shapes ($X$ and $Y$). In $Figure 1$, $X$ is “visually above” $Y$, and that’s why we can’t see part of the $Y$ ...
0
votes
1answer
52 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
votes
1answer
16 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 ...
0
votes
0answers
36 views

Apollonian Circles

I've been asked by my further maths teacher to research Apollonian circles and how the way Apollonius treated circles was different to the ordinary way using a centre and a radius. All the information ...
-6
votes
0answers
34 views

What is the largest diameter

What is the largest diameter of the bullet , if the box size 24 * 24 * 24 cm balls fit nine such. Somewhere somehow about. Up to ... And in all three dimensions. It turns out that half the diagonal ...
2
votes
4answers
106 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 ...
1
vote
1answer
43 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
vote
1answer
53 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 ...
-1
votes
1answer
32 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 ...
0
votes
1answer
22 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
1
vote
1answer
19 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 ...
2
votes
2answers
40 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
votes
1answer
19 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" $D$ ...
1
vote
2answers
27 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 $PR^2=a^2+c^2+2ac\cos\theta$. ...
0
votes
3answers
58 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 ...
7
votes
3answers
653 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 ...