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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1answer
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Finding the points of a circle by using one set of coordinates and an angle

I know the image below isn't to scale and that the angle isn't quite at the centre point but can we just imagine it is picture perfect.... I know the coordiantes and point (x,y) lets say they are ...
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4answers
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Name of the Angle of a unit circle's radial line from the positive X-axis

For the unit circle on a X-Y plane, is there a name for the Angle a radial line makes with the positive X-axis? The closest name that I can get from Wikipedia is a 'Central Angle' ( ...
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1answer
79 views

Circles partitioning the plane [duplicate]

What is the equation for the maximum number of regions into which N circles can partition a plane? Is there a name for this equation? A single circle partitions the plane into two regions, inside ...
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1answer
71 views

How to find the coordination of a tangent point on a circle?

I have a circle with the radius R, and coordinates of point A outside of the circle, and the coordinates of the center of the circle. I need to find the exact touching point of the tangent from point ...
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2answers
661 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
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1answer
79 views

Does an infinite collection of circles accumulates at a circle?

There is an infinite collection of closed circles in the plane, all within a finite bounding square. Does it contain an infinite sequence of circles that converge to a circle? Assume that a point is ...
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1answer
520 views

How to find the “as the crow flies” distance between two points that lie on a circle?

So I heard what I thought was a clever answer to "How do you make 2+2=5?".. On a 9-mile long circular track, drive two miles, then two more miles. You will be 5 miles from your start position. ...
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3answers
146 views

How to check whether a line exists inside a circle or not?

I have a line equation in the form of ax + by +c = 0. And I have a circle with radius r. I want to know whether the line exists inside the circle or not??
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3answers
341 views

equation of tangent to a circle with zero gradient

Find the equation of the tangent to the circle $$(x-3)^2 + (y-2)^2 = 1$$ at the point $(4,2)$. I cannot show the working of the tangent equation as gradient/slope = 0. So how can I find the gradient ...
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1answer
157 views

hyperbolic geometry (and circle ) construction problem

Was thinking about hyperbolic geometry, the Poincare Disk Model and Sweikarts constant and combined them all in a construction puzzle that I was unable to solve. My construction puzzle: Given: A ...
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0answers
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Rounding Corners: How to calculate Fillet radius?

How do I find the maximum rounding I can apply to either corner for any amount of rounding on the other corner? The all circles are perfect circles, but I can't figure out the max size of the ...
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1answer
69 views

Geometrically prove that for a point on a diameter…

Geometrically prove that for a point on a diameter between the center point and the perimeter of a circle, the distance between this non-center point is the shortest distance to the perimeter. So $A$ ...
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2answers
431 views

Paramtrizing a counterclockwise circle vs. a clockwise one

Does it make a different when you parametrize a counterclockwise full circle and a clockwise circle in the complex plane? For example, I am looking at computing an integral $\int_\gamma ...
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2answers
411 views

Formula for semi circle with diameter up?

So I know the formula for a semi circle is $$y = \sqrt{r^2 - x^2}$$ However, what if I wanted to find the equation for a semi circle who's diameter is at the top of the graph? Would this be the ...
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1answer
546 views

Locus of center of circle.

Consider two circles with radii $a$ and $b$ and centers $(a, 0)$ and $(b, 0)$ respectively with $0 < a < b$. Let $c$ be the center of any circle in the crescent shaped region M between the two ...
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3answers
2k views

Angle between tangents and angle subtended by radii are supplementary

Using the result that the length of the tangents draw from an external point to a circle are equal, prove that the angle between the two tangents drawn from an external point to a circle is ...
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1answer
104 views

Find the length of the common chord $PQ$

Two circles with centres $O$ and $O \ '$ of radii $3$ cm and $4$ cm, respectively intersect at two points $P$ and $Q$ such that $OP$ and $O \ 'P$ are two tangents to the two circles. Find the length ...
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1answer
253 views

Linear distance is proportional to angular distance, why?

Im my Fourier series book, the following is stated: We may specify the position of a point on the circle by its angular coordinate $\theta$, measured from some fixed base point. Since linear distance ...
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1answer
1k views

Two circles touch internally

Hello I've bean practicing for competition in math and can't seem to solve this problem,tried drawing chords,tangents,finding equal triangles,but couldn't seem to solve it.Any help would be ...
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1answer
90 views

Prove $\Delta APB $ is equilateral triangle

From a point $P$, two tangents $PA$ and $PB$ are drawn to a circle with centre $O$. If $OP$ is equal to the diameter of the circle, show that $\Delta APB $ is equiltateral. So this is the figure: I ...
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3answers
149 views

Show that the line $3x-4y=25$ and the circle $x^2+y^2=25$ intersect in two coincident points.

Show that the line $3x-4y=25$ and the circle $x^2+y^2=25$ intersect in two coincident points. What does two coincident points mean?
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1answer
166 views

Newbie: Find the intersection of a line and a circle and interpret geometrically

Find the points of intersection of the line $x+y+k=0$ and the circle $x^2+y^2=2x$. Show that there are two points of intersection if: $-1-\sqrt2<k<-1+\sqrt2$, one point of intersection if: ...
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1answer
485 views

Numerical integration of a region bounded by an ellipse and a circle

Consider an ellipse (say with major axis $a$ and minor axis $b$) centered at origin with a concentric circle of radius $R$. Area of the region between the circle and the ellipse is $$A = \pi R^2 ...
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0answers
42 views

Largest possible open circle inside an open circle?

When you construct the largest possible open circle within another open circle, can the radii of both circles be equal to each other? Or does the inner circle need to have a radius strictly < the ...
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1answer
636 views

Arc Length from chord and tangent angle

This is for a rubberband-powered car competition. In the diagram above, I will be given the length from points A to B, as well as angle a. The car will need to go from A to B, positioned at a to ...
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1answer
84 views

How to minimally move circles so that they don't overlap?

You're given a set of circles, all the same radius, residing at different locations in a 2d space. Some circles are in fixed positions. How do you make sure none of them overlap, minimizing the ...
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1answer
52 views

Given 3 points and there distances from eachother find a fourth point equidistant to the 3.

This question can also be asked: given a triangle, and its dimensions, whose vertices lie on the edge of a circle find the radius of the circle. I am not actually sure if there is enough information ...
2
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1answer
270 views

How do I calculate a point's coordinates on a circle’s circumference

I have got a circle with radius $r$ and center point $c_x$ and $c_y$. Known values: - $c_x$ and $c_y$ - $r$ - length $AR_a$ - length $BR_b$ Angle between point $A$ and the radius $r$ is unknown ...
2
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1answer
185 views

How do I calculate the angle to place rectangles side by side around a circumference?

I have a circle with radius $r$ and several rectangular objects. All rectangles have the same sides $a$ and $b$ (although the side $a$ may be different from side $b$). I would like to place the ...
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2answers
26 views

How will I get the point of intersection?

I'm confuse on how will I get the point of intersection of these two equations: $x^2+y^2+5x+y-26=0$ and $x^2+y^2+2x-y-15=0$ I tried using the elimination method but I can't get it.
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1answer
442 views

Finding the radius, distance of the center of circle inscribed in the square

I am trying to solve this question but can't figure out the last part. I was able to get answers for part A and B but i don't know how to approach/solve part C. Any help will be appreciated. The ...
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1answer
176 views

Radius of circle by knowing a cross section.

I have a curve on an ellipse where I know the length of a cross section and need to find out it's radius (vertically and horizontally) and calculate the angle of the curve. In the following diagram ...
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3answers
685 views

How do you prove arc length is greater than chord length?

Graphically, it's obvious that given two different points $a$ and $b$ on a circle of radius $r$, the linear distance (chord length) from $a$ to $b$ is less than the arc length from $a$ to $b$. How do ...
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2answers
143 views

Equation of the Circle

How to find the equation of a circle if the givens are the: Case 1: Tangent to $2x + 3y + 13 = 0$ and $2x - 3y - 1 = 0$; contains $(0,4)$ Case 2: Tangent to $x - 3y - 7 = 0$ and $3x + y - 21 = 0$; ...
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5answers
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Three circles within a larger circle

Let's say that the radius of the bigger circle is R. Every circle inside touches the perimeter of the bigger circle and two other circles. How to find the radius of the smaller circles (all are ...
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2answers
106 views

Finding the area of a portion of circle

How to find the area of green region? Angle between centre $A$ of first circle and the radius is given as alpha. Distance between $A$ and $B$ is $d$. Radius of two circles is $R$. Can the area be ...
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1answer
434 views

Thinking outside of the box

You want to draw a circle with a 4 inch radius. A trivial task for you and your trusty compass. When you go to grab your compass which has not had much love for a while you find it is rusted shut; ...
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2answers
718 views

Radian and the length of a chord of a circle

Question In a circle of radius $r$, an arc of it is $2S$ long. Find the length of the chord corresponding to that arc (AB in the diagram below) . Details I got this question in a math test. And ...
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10answers
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Find the approximate center of a circle passing through more than three points

Consider n point $(x_1,y_1), (x_2,y_2),\ldots, (x_n,y_n)$. For $n = 3$ it is easy to find the center of the circle passing through the three points. I wanted find the approximate center of the ...
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1answer
101 views

Intersecting circles and their angles

There are 3 tangent circles: Now we move circles A and B such that they intersect C but do not intersect each other: In the figure, the angle near C increases. Will this always be the case? I ...
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1answer
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Finding equation of the image under a linear transformation

The equation of C is $x^2 + y^2 =1 $ How do I find the equation of the curve $C'=f(C)$ This is the image of $C$ under the linear transformation $f$ represented by the matrix $A=\begin{bmatrix}2 & ...
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0answers
233 views

Calculating center line of curved pipe

I want to have have a disk move vertically through a curved pipe. The pipe shape and size will be constant, the overall position and rotation in a 3d space will be random. Is it possible to calculate ...
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2answers
76 views

How $\pi$, $3.1415…$ and $180^o$ are adaptive together?!

I planed following to compute the circle's circumference. The circle's circumference finally can computable from: $$\lim_{\alpha\to0}{\frac{360^o}\alpha d} = 2\pi r$$ I don't want to follow above ...
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2answers
73 views

Question on inscribed equilateral triangle

Question: $ABC$ and $ODE$ are equilateral triangle with $BC || DE$. If $O$ is the center of the circle, then find the ratio $AQ:QC$ So, my thought on this is that, since we are not given the ...
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Find a circle's radius with three known tangent lines

I need to find the equation for a circle (mainly its radius) which is tangent to the following three lines: $y = 0$ $y = \tan(70)x$ $y = -1.428148x + 0.790201$ For the last tangent line equation, ...
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1answer
139 views

Find the shaded area

Find the shaded area Here is the equation that i've made \begin{align*} S&=\pi R^2\\ S_1&=\pi {R_1}^2\left(\frac{24}{360}\right)\\ S_2&=\pi{R_2}^2\left(\frac{24}{360}\right) \end{align*} ...
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3answers
704 views

Find radius of a circle which is tangent to three known lines

I need to find the equation for a circle which is tangent to the following three lines: y=0 x=0 y=-x+0.338334 For the last tangent line equation, I know that it is tangent at the point (0.169167, ...
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4answers
67 views

Trouble in this circle question

Referring to this diagram (self-made): Question says: In the given figure diameter of the circle is $3$ cm. AB & MN are two diameter such that MN is perpendicular to AB. In addition CG is ...
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1answer
162 views

Great circle and how to “imagine” it in this case?

I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be. A satellite ...
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3answers
528 views

Equation of a circle with radius and contains 2 points

Find the equation of the circle with radius $5$ and contains the points $A(-8,0)$ and $B(-4,-2)$ Hint: Equate radii. Thats the question from my midterms exam, can anyone help me finding this one, ...