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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3answers
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Problem based on circle geometry - related to circumcircles and angles finding the angles within a circle

Let the vertex of an angle $ABC$ be located outside a circle and let the sides of the angle intersect equal chords $AD$ and $CE$ with the circle. Prove that the angle $ABC$ is equal to the half the ...
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1answer
21 views

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$ [on hold]

Find the equation of locus of a point which is at a distance $5$ from $A$ $(4,-3)$. Could some explain how to solve this in detailed.
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1answer
32 views

Two tangents BC and BD are drawn. Prove that Ob=2BC

Two tangent segments BC & BD are drawn to a circle with centre O such that $\angle$CBD=120$^{\circ}$. Prove that OB=2BC. What I've tried, BC=BD[two tangents drawn from a single point to the ...
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2answers
20 views

Algorithm to cover maximal number of points with one circle of given radius

we have a plane with some points on it. We know coordinate of each point apriori. We also have a circle of unit radius. I need an algorithm that determines optimal/sub-optimal position of a circle ...
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3answers
34 views

How to make a semicircle graph?

What is the formula to make a semicircle graph that is continuous? By continuous I mean like a sine or cos graph but shaped like semicircles one after the other. Thanks
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1answer
31 views

Is the Locus circle?

Locus of points such that sum of it's distances of them from four fixed points remains constant? Is the locus circle? I was not able to solve it as there were four radicals. Is it a theorem?
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2answers
31 views

A question an normal to the circle

The equation of the normal to the circle $(x-1)^2+(y-2)^2=4$ which is at a maximum distance from the point $(-1,-1)$ is (A) $x+2y=5$ (B) $2x+y=4$ (C) $3x+2y=7$ (D) $2x+3y=8$ Since its a ...
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1answer
44 views

Power series converging at the convergence radius

Let $f(z)=\sum a_nz^n$ be a power series of radius $R$. By Abel' radial theorem, if $f(R)$ converges then $f$ is continuous over real numbers at $R^-$. I had some questions on how that can be ...
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0answers
30 views

Length measurement [duplicate]

I need to find the length of thread that is winded in a bobbin. I tried to find out with the rotation of the shaft. but as the diameter of the bobbin (with thread) increases the length winded is also ...
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1answer
20 views

Find the equation of the radius

Find the equation of the radius of the circle $x^2-4x-6y+y^2=23$ and passing through the point $(4,5)$. My attempt: Here the equation of the circle is: $$x^2-4x-6y+y^2=23$$ $$(x-2)^2+(y-3)^2=6^2$$ ...
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7answers
1k views

Length of a Chord of a circle

I was wondering about the possible values that the length of a chord of a circle can take. The Length of a chord is always greater than or equal to 0 and smaller ...
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0answers
34 views

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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0answers
34 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
34 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
33 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 ...
2
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1answer
47 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
35 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
34 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 ...
0
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1answer
30 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
20 views

how to find this sector angle

Given a circle with r is equal 2cm, can we find the sector's angle?
4
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2answers
55 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 $|CB|=b$. [closed]

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 ...
0
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1answer
39 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
45 views

Area stacked between common tangent and circles [closed]

Is there any way to find area of shaded region? The radii of circles are $4$ and $12$ units.
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1answer
28 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 ...
2
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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
42 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) ...
2
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2answers
55 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
56 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
38 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
43 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
32 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
40 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
82 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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1answer
26 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
49 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
48 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
36 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
14 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
75 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
51 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 $C_2: (x+6)^2 + (y+2)^2 = 9$? $3$ ...
1
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3answers
57 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
53 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.