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

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Circle Geometry - Proving Question

Suppose $C$ is any point on a circle, above a diameter $AB$. $P$ and $Q$ are points on the minor arcs $\widehat{AC}$ and $\widehat{BC}$. Prove that $$\angle APC + \angle CQB = \frac32\pi$$ Currently ...
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arrange div elements in circle and square

I n number of divs which are arranged in a circle using javascript. Right now i set the dimension of each div to 40*40. Below is what i am able to achieve so far. This is how i find X & Y of each ...
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148 views

Sketching graphs of circles.

A circle graph function is in the form of $x^2 + y^2 = r^2$ If I am asked to graph $(x-2)^2 + (y - 1)^2 = 4$, do I have to solve for x and y to graph first?
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132 views

Alternative form of equation of circle?

In a problem set I was solving, one of the solutions used the equation of a circle in the form $$(x-h)^2 + (y-k)^2 + \lambda(ax + by +c) = 0$$ where, $(h,k)$ is any point on the circle $ax+by+c ...
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18 views

Bertrand paradox Random midpoint

http://en.wikipedia.org/wiki/Bertrand_paradox_(probability) The link above explains Bertrand paradox in probability. In "Random Midpoint method" Bertrand uses a concept that all chords whose ...
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45 views

Find the locus of $2/z$ given that $|z-(1+i)| = 2$

If complex numbers $z$ satisfy the equation $|z-(1+i)| = 2$ and $\displaystyle \omega = \frac{2}{z}$, then locus traced by $\omega$ in complex plane, is ... My try I want to solve it ...
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76 views

Calculate center of circle tangent to two lines in space

Good afternoon everyone! I am facing a problem which is straining my memory of linear algebra. I have: Three points with known coordinates, forming a triangle in space. Let the coordinates be ...
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70 views

Problem of a circle tangent to three other circles

Two circles with centres A and B and radii 14 and 7 units respectively touch each other externally. M is the mid point of segment DE and is the centre of the circle with radius 21 units. The two ...
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14 views

$L=R\alpha=R({H^4\over32R^4}-{H^2\over4R^2}-{1\over2})$

Let $XY$ be a diameter of a circular pond of radius $R$. A vertical pole of height $H (H < 2R)$ is erected at $Y$ . An observer at $X$ finds that the angle of elevation of the top of the pole is ...
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40 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
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48 views

Finding three collinear points passes through three circles

Assume that we have three collinear points $A(x_0,y_0),B(x_1,y_1)$ and $C(x_2,y_2)$. They are on three different circles whose centres and radii are respectively $\big((P_x, P_y), r_P\big)$, ...
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31 views

Finding the side lengths of a rectangle given a circle passing through one of its vertices and touching two of its sides

A circle touches a rectangle $ABCD$ of side lengths $2a$ and $2b$ at $M$ and $N$ on sides $AB$ and $AD$ respectively. It also passes through the point $C$. If the perpendicular distance of the line ...
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1answer
12 views

What does the locus of $M$ form?

Let $A$ and $B$ be two fixed points on a fixed straight line. Two circles touch this line at $A$ and $B$ respectively and tangent to each other at $M$. When the circles vary, what does the locus of ...
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36 views

Complex Number and Geometry

Given $A(3+4i)$, $B(-4+3i)$ and $C(4+3i)$ be the vertices of a triangle $ABC$ which is inscribed in a circle $S=0$. Let $AD, BE, CF$ be altitudes through $A, B, C$ which meet the circle S=0 at ...
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39 views

Crazy rectangles, semi-circles, and circles!

Problem is to find the ratio of the area of the circle to that of the semi-circle. Note that points $F$ and $E$ weren't given in the original diagram, and that the circle at the top-right ...
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41 views

Horses grazing in a circle.

Question: Diagram: Note that The circle with center $C$ is touching the arc of semi-circle $AB$ also; I couldn't draw it. The figure wasn't drawn on cartesian planes; so, though it may seem ...
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23 views

Locus of the centre of a circle $\Gamma$

Let $\Gamma_1,\Gamma_2$ be two circles centred at the points $(a,0),(b,0);0<a<b$ and having radii $a,b$ respectively.Let $\Gamma$ be the circle touching $\Gamma_1$ externally and $\Gamma_2$ ...
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22 views

Determine the length of **DC** in terms of $l_1$ and $l_2$

In the given figure, E is the midpoint of the arc ABEC and ED is perpendicular to the chord BC at D. If the length of the chord AB is $l_1$, and that of BD is $l_2$, determine the length of DC in ...
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2answers
50 views

Finding the angle between the $2$ radii of a circle

Consider a circle with centre $O$. Two chords $AB$ and $CD$ extended intersect at a point $P$ outside the circle. If $\angle AOC = 43^\circ$ and $\angle BPD = 18^\circ$, then what is the value of ...
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18 views

How to compute an angle from arbitrary limits (min and max) and a default value?

My question is about a software problem but I think it's more related to Math equations. I'm developing a round knob which is limited to 315deg with a 45deg unused part of the knob. I have some ...
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2answers
36 views

Interior point of $\Delta\,ABC$

if $P(\lambda,2)$ is an interior point of $\Delta\,ABC$ formed by the lines $$x+y=4$$ $$3x-7y=8$$ $$4x-y=31$$ Find $\lambda$ My Idea: The vertices of $\Delta ABC$ are $A(\frac{18}{5},\frac{2}{5})$ ...
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85 views

Circumcircle of an isosceles triangle and length relation

I was asked to prove the following problem. Consider the following diagram where a triangle $ABC$ lies inside its circumcircle, $D$ is the point where the angle bisector $\alpha$ of $B$ intersects ...
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38 views

is diffrence of raduis of 2 circles is not depend upon thier peremeter

I read on the Internet it's true, but I suspect it: Image describing the puzzle Take a ribbon tightly wound around the equator of the earth. Add 1 meter to that ribbon by cutting it at any ...
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2answers
21 views

Determine if circle contain point ( geographic ) while the number before the point are equals

I want to check if circle contain some point(latitude and longitude). the problem I have is that the number before the point are equals, for example: ...
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1answer
75 views

Formula to calculate a side of triangle with given angle

I have triangle like in the picture. The known angles: α (total angle of the I-J-K2 triangle) b (total angle of the I-P2-K2 and I-P1-K2 triangles) The known 3D points with X,Y,Z-coordinates: ...
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48 views

Family of circles touching a line

I found this in a book but I am not able to understand how they got this result. It goes the equation family of circles touching a given line $(y-y_1)=m(x-x_1)$ at $(x_1,y_1)$ for any value of $m$ is ...
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28 views

Prove in a cyclic quadrilateral ${AC\over BD}={{ps+rq}\over pq+rs}$

Let $ABCD$ be a cyclic quadrilateral with length of sides $AB=p$, $BC=q$, $CD=r$, and $DA=s$. Show that $${AC\over BD}={ps+rq \over pq+rs}$$
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31 views

Graphing a Circle that doesn't have two of each variable

Graph the circle: $$x^2+y^2-2x-15=0$$ I know how to approach this problem if there were two $y$ and $x$ variables. But there is only one $y$ variable. How would I approach this?
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29 views

Stereographic Projection of sphere through plane $ax+by+cz=d$

I have managed to pullback the equation for the plane to the $uv$-plane, but cannot manipulate it to make it look like a circle in $R^2$. My pullback is as follows: ...
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49 views

Finding a point on a circle that has a distance L (arc length) from another point

Given the coordinates of a single point on a circle and a length of an arc $L$, how do I find the coordinates of another point? Or, to put in another form: I have the radius $r$, the length of the ...
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130 views

Proof of “Japanese Theorem” — Triangulation of Cyclic Polygon

On Mathoverflow, I saw this great result on the "Japanese Theorem". “Japanese Theorem” on cyclic polygons: Higher-dimensional generalizations? Given triangulation of a cyclic polygon, the sum of ...
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187 views

Maximum speed in a circular orbit?

Visualize two points:  $O\equiv(0\mid 0)$ and $D\equiv(d\mid 0)$.  The two are $d$ units apart.  Visualize a movable rod whose endpoints, $C_O$ and $S_O$, are a unit apart. $C_O$ always coïncides ...
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How to find distance between two different circles

I am trying the find the distance between two different sized circles, both centred on the horizontal plane. I know the diameter of each circle, and the length around both circles if wrapped like a ...
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Find the two lines from a given slope that are tangent to a given circle

Guys please teach me how to solve this one. I want to learn. The question is find an equation of each of the two lines having slope -4/3 that are tangent to the circle x^2 + y^2 + 2x -8y - 8 = 0.
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Finding an equation of a circle with a given center and a tangent line.

My math homework is finding an equation of the circle. Given that the center is at (-3,-5) and tangent to the line 12x + 5y =4. I don't know how to solve this since our professor didn't teach this to ...
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1answer
41 views

Two circles intersection

Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is ...
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1answer
66 views

Two circle intersection

Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points?
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31 views

Possible to square circle using additional tools?

So I just stumbled upon the wikipedia page for squaring the circle and learned that it's impossible to do with only a straightedge and compass. Is this possible if we are allowed to use any other ...
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3answers
156 views

Equation with k describing a circle

My equation is the following, and I would like to find which $k$ can make it a circle. $$x^2+y^2+4x-6y+k=0$$ My naive approach is to have $k$ to be $-4x+6y+c$ where c is any number, so that I can ...
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33 views

2 pi term in sinusoidal signal

My intuition is that the $2\pi$ term in the sinusoidal signal equation: $$x(t) = \sin(2\pi\,f\,t)$$ Is indicative of the fact that this signal can be described as movement around a circle, is that ...
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52 views

How do I calculate the height of a cross section of a circle?

I'm working on an LED lighting project and have discovered that it involves a little math... I'm mounting LEDs to plexiglass facing away from the surface I want lighted. I'm looking at cutting a ...
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1answer
154 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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angles subtending arcs at the circumference and centre

$A$ and $B$ are two points on the circumference of a circle center $O$. $C$ is a point on the major arc $AB$. Draw the lines $AC$, $BC$, $AO$, $BO$, and $CO$, extending the last line to a point $D$ ...
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circle measure - i don't know what method im supposed to apply

C(5,3) is the centre of a circle of radius 5 units. Show that this circle cuts the x-axis at A(1,0) and B(9,0) im guessing simply drawing it with a compass is not what im being asked here. i dont ...
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34 views

Solving angles within a cyclic quadrilateral

Please could you help with solving angles x and y as well as writing how you solved them.
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1answer
18 views

Finding the equation of a tangent of a circle at a point

The line with equation y=mx is tangent to the circle with centre (-8,0) and radius 4 at the point P(x,y) Show that $m=\pm\frac{\sqrt{3}}{3}$ and hence find the coordinates of P
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4answers
93 views

Integration for finding the Arc Length of Circle $x^2+y^2=a^2$

Question: Find the arc length of the circle given by $x^2+y^2=a^2$. $Ans = 2\pi a$ How to obtain the ans? I have no ideas after doing the following thing. Thank you for your ...
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2answers
57 views

Proving the inscribed angle theorem

I need to prove that a circle's inscribed angle is 1/2 of the arc it intercepts. I am given that one of the chords making up the angle is the diameter. I have an entire project to do based off of this ...
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66 views

How to create a two circle Venn diagram with 3 equal sections?

I had a student ask if I could draw a Venn diagram in which each region was of equal area. I have played around with this a little but have not landed on an answer I'm satisfied with. I was able ...
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1answer
40 views

3 circles and 3 squares all inscirbed into a right angled triangle problem

This is quite a tricky question for me, but this is how far I got: My drawing may not be precise, but I do know the points of tangency. I am a little stuck now, and I would appreciate a great hint ...