For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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Externally tangent circle coordinates

I am trying to program following case as show in figure below. I have two circles at (x1,y1) and (x2,y2). Having coordinates, we can mention that the two circles are making an angle \theta_2. I need ...
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22 views

Co-ordinate Parabola Circle Contained in it; Difference in maximum and minimum possible radius

If the Difference of radii of larget and smallest Circle passing through the focus of Parabola $$Y^2=4x$$ and toughing parabola in at least one point is My Approach Let Circle be $$C: ...
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3answers
28 views

calculate radius of circle that by given length of square that is inside it

in this picture a length of square edge is 8 cm. I want to calculate the radius of circle. i try to calculate it, but i don't know how. I calculate this:
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1answer
32 views

Showing that $\alpha$ satisfies the equation $\sin 2x=x$

This is an A level question. For better understanding, I will attach a screenshot of the question and the mark scheme. Question: Here's what I have done: $$A(OBA) = \frac 12r^2α$$ [basic ...
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1answer
43 views

Quarter Circle packing

Just today, I was making tortilla chips, and I began to wonder, what is the most efficient way to pack circular quarters onto the plane? This sort of circle packing is most efficient for circles, ...
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1answer
34 views

Is there a measure which allows me to tell how closely something is to an ellipse?

Roundness is the measure of how closely the shape of an object approaches that of a circle. I am trying to find a similar measure which shows how closely is something to an ellipse. Is there any ...
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0answers
32 views

Are all curves with equation of the form $(\xi x +n) \cdot x = \text{const}$ circles?

Let $x(t)=(x_1(t),x_2(t))$ with $t\in [a,b]$ be a smooth curve in $\mathbb{R}^2$ and $\xi \in \mathbb{R}$ such that $$(\xi x +n) \cdot x = \text{const}$$ Here $n$ is the unit normal to the curve. Is ...
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1answer
27 views

Deriving formula for externally tangent circle to internally tangent circle

($x^2+(y+1)^2=R^2$ should say $x^2+(y-1)^2=R^2$) I am trying to derive a formula for the radius of the circle that is externally tangent to the internally tangent circles of the quarter-circle, and ...
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2answers
19 views

how to find this sector angle

Given a circle with r is equal 2cm, can we find the sector's angle?
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2answers
50 views

How do I show that $n=2$ is the only integer satisfy :$\cos^n\theta+ \sin^n\theta=1$ for all $\theta$ real or complex?

It is well known that :$\cos²\theta+ \sin²\theta=1$ for all $\theta$ real or complex ,I would like to ask about the general equality :$\cos^n\theta+ \sin^n\theta=1$ if there is others values of the ...
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1answer
34 views

Find $|CM|$, if $|CA|=a$ and $|CB|=b$. [on hold]

Let $O$ be a center of a circle, circumscribed over $\triangle ABC$. Perpendicular, drown from the point $A$ on the line $CO$, cross the line $CB$ in the point $M$. Find $|CM|$, if $|CA|=a$ and ...
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1answer
38 views

Center point of 2 tangent circles along 2 tangent lines

Given points P1, P2, and P3, I need to calculate the center point of 2 tangent circles, C1 and C2, with radius R. Line P1P2 is tangent to circle C1 at P2, line P2P3 is tangent to C2, and C1 and C2 are ...
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3answers
44 views

Area stacked between common tangent and circles [on hold]

Is there any way to find area of shaded region? The radii of circles are $4$ and $12$ units.
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1answer
24 views

Compound angle formula

I understand how to use the compound angle formula when solving $\sin(\pi/12)$. However I dont understand how I can use a compound angle formula to show $$\arctan(3)-\arctan(1/2)=\pi/4$$ Thankyou Any ...
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3answers
54 views

Basic question about angles and measurement in degrees

I have a doubt related to angles which I am a bit embarrassaed to ask since I know is something of basic geometry, but nevertheless my question is the following: As I understand it, an angle between ...
4
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1answer
39 views

Drawing a circle tangential to 3 circles (internally to one of them)

The two small circles (in black) are equal in radius, and tangential to the large circle. They also touch each other at the center of the large circle. Now, I want to construct a circle (in orange) ...
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2answers
53 views

Proving volume of a sphere

I randomly decided to derive the volume of a sphere. The area of a circle is $\pi r^2$. So the volume, I thought, should be $\int \pi r^2 dr = \frac{\pi r^3}{3} $, summing up the area of many discs. ...
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1answer
22 views

Is part of a circle lying on first quadrant?

I have circle $ C: (x-x_0)^2+(y-y_0)^2\leq r^2$ with center $(x_0,y_0)$ and radius $r$. I want to find out in exactly what quadrants the circle lies. Is there a condition with this functionality? ...
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2answers
52 views

Find intersection point of 3 circles

so first of all, I just want to point out that I am a beginner, so cut me some slack. As the title says I have 3 circles. I know the coordinates of each center and the radius of each circle. What I ...
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2answers
36 views

I need some help with Geometry. Is this a correct answer to this problem?

Good day, I have a question regarding geometry. I don't know whether my answer is correct because the answer in my book uses a totally different method for solving this particular problem. Here's ...
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2answers
42 views

Complex Analysis: Show that $\int_{\gamma}\frac{1}{(z-a)(z-b)}dz=\frac{2\pi i}{a-b}$ [closed]

How can I show that if $|a|<r<|b|$, then $\int_{\gamma}\frac{1}{(z-a)(z-b)}dz=\frac{2\pi i}{a-b}$, where $\gamma$ is the circle with center the origin, radius $r$, and positive orientation? ...
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1answer
31 views

Dividing Up A Circular Search Area

BACKSTORY: I need to collect 500 plant samples for strontium analysis. The samples are randomly distributed across a circular area with a radius of 300 kilometers. I have to do this in 30 days, so I ...
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1answer
39 views

The area of $KPMQ$

On the hypotenuse $AB$ of triangle $ABC$, with $\angle C =90^{\circ}$ and area $S$, as on the diameter, was drawn a circle. The points $K$ and $M$ were chosen on arcs $AB$ and $AC$ respectively, in ...
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2answers
79 views

2015 AMC 10A Problems/Problem 14

The Clockblock Problem - problem and solutions I'm preparing myself for AMC 10 (which I'm sure a lot of other students would be doing too), but then I just don't know how to solve this problem (and ...
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0answers
27 views

Rotating a 2d equation in a 3d space? [closed]

I'm attempting to rotate a shape taken from a parametric equation. I'm doing this inside a Java program, so it automatically adjusts the variables as I need. I have: $t = \pi$ but t decreases in ...
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1answer
25 views

Prove that if tangent of $x^2+y^2=a^2$ is $px+qy=1$, then $(p, q)$ is on a circle

It's actually my textbook problem so I have seen a proof in my class but that doesn't satisfy me. The proof was given by the condition that if $px+qy=1$ is a tangent then the distance from the center ...
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2answers
48 views

Finding the equation of a circle from the equation of its tangents

Given the equation of a pair of lines : $36x² - 63xy + 20y² + 54x - 17y - 10 =0.$ If the circle touches one of the lines at (-3,-1) and the other at some point then find the equation of the ...
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1answer
26 views

Equation of a circle whose radius and tangent is given

Equation of a circle which passes through the origin, whose radius is $a$ and for which $y = mx$ is a tangent.
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3answers
47 views

Circle through the circumcentre of a triangle problem

Let ABC be an acute triangle and O it's circumcentre. Let S denote the circle through A,B, O. The lines CA and CB meet S again at P and Q, respectively. Prove that the lines CO and PQ are ...
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2answers
36 views

Find the intersection of a vertical line segment in a circle.

My brother needs help coming up with a formula for a problem that I already did but failed to write out the formula for. The problem is: Consider a circle with the point (5,4) and a radius of 3. ...
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2answers
33 views

points of intersection of two circles and area of intersection relationship

if the points of intersections of two circles are defined(known), how can these points used to decide if a given point p is inside an overlapped area or outside it ? in other words, can we make any ...
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1answer
13 views

Circle equation in homogeneous coordinates

Can someone give me a derivation why the circle equation is expressed in homogeneous coordinates like this (as described in Hartley): $$ (x-a\cdot w)^2 + (y-b\cdot w)^2 = r^2\cdot w^2 $$
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0answers
74 views

Stacking circles

When I tried to stack 21 circles of radii $(30, 31, 32... 50)$ on top of each other in a tube (ID of $100$ wide), I thought they would reach the same height regardless of the order, however I was ...
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2answers
20 views

Equilateral hexagon and a Circle

In the following diagram $ABCDEF$ is a equilateral regular hexagon with $AB = 1$ A circle is drown with radius $2$ with point $E$ as a center. What is the area of the shaded region of the circle ...
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4answers
1k views

What is the area of the circle?

In the following diagram, $AB = 4$ and $AC = 3$. What is the area of the circle? I can't find any way to solve this.
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1answer
30 views

Number of chords having integral length

A point $P$ lies inside a circle centered at $C$ such that $CP=6$. The radius of the circle is $10$. Find the number of chords passing through $P$ which has integral length. Attempt: One solution ...
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4answers
50 views

Equation of a circle tangent to two lines , given the radius . [closed]

What is the equation of the circle whose center is in the first quadrant and with the radius of $4$ units, given that it is tangent to the $x$-axis and to the line $4x-3y=0$?
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1answer
40 views

Circle, tangent, distances

Straight line $L: 2x - y +k = 0$ is the tangent of a circle $C_1: x^2 +y^2 = 5$ , if $k <0$, What is the shortest distance between $L$ and another circle $C_2: (x+6)^2 + (y+2)^2 = 9$? $3$ ...
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3answers
55 views

Common area between Circle and Equilateral triangle [closed]

A circle is drawn with diameter BC of a equilateral triangle ABC. Area of triangle is $\pi - 3$ less than the area of the circle. What is the area of the common region between circle and the triangle? ...
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1answer
52 views

Find the equation of a circle which…

The circle touches the line $y=2$ , passes through the origin and the point where the curve $y^2-2x+8=0$ meets the x-axis.
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2answers
35 views

Why are both $|z-z_0| = r$ and $|z-z_0|^2=r^2$ equations of a circle?

Why are both $|z-z_0| = r$ and $|z-z_0|^2=r^2$ equations of a circle? Specifically, why would the latter one describe the same circle as the former one?
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1answer
31 views

Parametric problem with circumference and tangents

Given the circumference $(x-3)^2+(y-2)^2=13$ find $k$ where $k$ is a coefficient in the parametric equation $(k+1)x+8ky-6k+2=0$ of the lines passing through the points $A(0;4)$, $B(6;4)$, $C(1;-1)$. ...
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1answer
39 views

The equation of a circle on a complex plane?

The equation of a circle $|z-z_0|=r$ in a complex plane has (among others) the form: $$z\overline{z}+\overline{b}z+b\overline{z}+c=0$$ where $b=-z_0 \in \mathbb{C}$. What I'd like to understand is, ...
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0answers
35 views

Finding the centre of a circle

I am trying to find the centre of the equation mentioned in part c), but I can only really understand the "long way" of doing it (i.e., finding the intersection of the prependicular bisectors of $PT$ ...
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1answer
26 views

find max of total area of solenoid

I'm having problems findind the best way to maximize the total area of my solenoid, of course given $l$ as the costant value of the total lenght of my wire. I can't find it on the internet, so I'm ...
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2answers
41 views

Coordinates of circumcentre of an isosceles triangle in 3D

I have an isosceles triangle in 3D and I need to find the coordinates of the circumcentre of this triangle. I know the coordinates of the three vertices. One method I thought of is to solve equation ...
2
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1answer
43 views

Find radius such that packing circles into a fixed rectangle maximises total area of circles

I want to pack equal-sized circles into a rectangle with width $w$, and height $h$. The total area of all of the circles should be maximised. the radius of each circle can vary, but is contrained; ...
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2answers
34 views

finding the radius of the circle given a coordinate

find the radius of the circle with center at (-1,2) if a chord of length 10 is bisected at (4,-3).(this is exactly what our professor given to us) im thinking of using the distance formula which is ...
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3answers
44 views

Find the center of circle given two tangent lines (the lines are parallel) and a point.

How to find the center of a circle if the circle is passing through $(-1,6)$ and tangent to the lines $x-2y+8=0$ and $2x+y+6=0$?
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32 views

Oval Clock, How to find the points on the edge of an Oval?

I know the length (l), height (h), and center point C(0,0) of my Oval. I am looking to find a way to find a point on the edge of the oval. It's for an oval clock I'm building in java and the hands go ...