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

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0
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3answers
14 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
14 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 ...
0
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0answers
95 views

Translation request: geometry problem stated in Korean [on hold]

Please im a foreing studying in south korea.. so i dont understand nothing in class... can any one tell me what is this called in english? thanks
1
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2answers
18 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
38 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 ...
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votes
1answer
23 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
33 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
29 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 ...
0
votes
0answers
17 views

How to draw an arc with varying thickness [closed]

Arc with various thickness in detail I need to draw an arc in android with varying thickness, as represented in the below image, Is it possible to draw an arc and clip it? as the arc can be ...
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 ...
1
vote
0answers
41 views

Will someone check my project data? [closed]

I conducted an experiment where I gathered data to find out how many m&m's would be needed to cover the top of a pie with a 10 foot diameter. I drew my own circles and put as many M&M's as I ...
4
votes
4answers
83 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
32 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
54 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
24 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
28 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
97 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
129 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
11 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
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0answers
8 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
46 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
15 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
33 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
101 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
42 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
49 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
21 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
39 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
55 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
648 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 ...
0
votes
1answer
20 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: $$ ...
1
vote
0answers
40 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 ...
-1
votes
0answers
20 views

question based on property of circle

A circle is inscribed in triangle $ABC$.The radius of circle is $4$ cm. $CD=6$ cm and $BD=8$ cm.(where $D$ is the point of contact of $CD$ which is an side of triangle $ABC$) Find AC and AB.
2
votes
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
votes
2answers
125 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 ...
0
votes
1answer
27 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 ...
1
vote
1answer
24 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
votes
1answer
92 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
votes
5answers
277 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) ...
1
vote
0answers
48 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 ...
-1
votes
2answers
45 views

Circle in Triangle Help! [closed]

P is the center of the inscribed circle of right triangle ABC. If AB=4 and AC=2 , find AP.
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votes
1answer
20 views

Circle Angle Help! [closed]

In the figure below, XY, YZ, and XZ are chords and WV is tangent to the circle at X. If the measure if angle Z=38, find the measure of angle YXV.