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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2answers
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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
53 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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0answers
42 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 ...
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2answers
77 views

How to solve this semi-circle problem? [closed]

The figure above shows a semi-circle. $\angle BAP$ is $\alpha$ radian. The area of semi-circle is bisected by $AP$. Prove that $$2\alpha+\sin 2\alpha = \frac{\pi}{2}$$ I have simply no clue ...
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0answers
10 views

Time for finite beam to cross a point in circular region

I'm trying to find the time a finite width beam takes to cross a point in circular region. Assuming the beam width at distance $r$ from the center is some constant times $r$, $kr$. I have calculated ...
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3answers
33 views

Radians/second question [closed]

I'm stuck on this circle question that my cousin in high school asked me and basically, I need clarification on what I remember should be fine-> tire has radius of 42.5 cm rotating 3500 ...
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2answers
57 views

Find the locus of the midpoint

Find the locus of the midpoint of the chord of the circle $x^2 + y^2=a^2$ which subtends a $90°$ angle at point $(p,q)$ lying inside the circle. I tried to solve it by taking that let the chord ...
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3answers
479 views

Is the metric on the circle, induced from the plane, not a flat one?

My question concerns the highlighted part posted below, from Wikipedia article. (Link to the revision at the time of this post.) I'd say I can't detect the curvature of the unit circle if I go along ...
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2answers
38 views

A sector of a circle has the area of 12 cm squared. If the angle at the centre is 60 degrees, calculate the diameter of the circle.

The answer I got was $45.8$cm but it seems wrong. I did $$ A=\pi r^2 $$ $$ 12= \frac{60}{360} \pi r^2 $$ $$ \frac{12}{\pi} \cdot \frac{360}{60}=r=22.9183118 $$ $$ d=45.8 $$
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0answers
30 views

On the existence of a continuous section of $\zeta\in\mathbb{S}^1\mapsto(\zeta^m,\zeta^n)\in\mathbb{S}^1\times\mathbb{S}^1$.

Let $(m,n)\in\mathbb{Z}^2$ and let define the following map: $$f:\left\{\begin{array}{ccc} \mathbb{S}^1&\rightarrow&\mathbb{S}^1\times\mathbb{S}^1\\ \zeta&\mapsto&(\zeta^m,\zeta^n) ...
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1answer
31 views

find the possible range of values for k for circles not touching

Circle 1 C has equation ${(x + 1)^2 + (y - 1)^2}$ = 121 A circle 2 C with equation ${x^2 + y^2 -4x + 6y + p = 0}$ is drawn inside 1 C . The circles have no points of contact. What is the range ...
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2answers
27 views

Locus of point of intersection of tangents at $A$ and $B$

From a Point $P$ on $C_1 \equiv x^2+y^2=9$ two tangents are drawn to $C_2 \equiv x^2+y^2=1$ which meets $C_1$ at $A$ and $B$. Find the Locus of point of intersection of tangents at $A$ and $B$ on ...
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2answers
31 views

Prove length of arc is the same as chord when $\theta$ tends to $0$

I'm trying to prove that the length of an arc is the same as the length of a chord in a circle when $\theta$ tends to $0$. Let $$ \begin{eqnarray} arc &=& \theta \\ chord &=& \sqrt{(1 ...
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2answers
39 views

A right angled trapezium is circumscribed about circle.What is the radius of the circle,if the lengths of the bases are $a$ and $b.$

A right angled trapezium is circumscribed about circle.What is the radius of the circle,if the lengths of the bases(i.e. parallel sides ) are $a$ and $b.$ By using the property that the length of ...
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1answer
21 views

In a triangle $ABC$,$AD,BE,CF$ are the altitudes and $R$ is the circumradius,then find the radius of the circle $DEF.$

In a triangle $ABC$,$AD,BE,CF$ are the altitudes and $R$ is the circumradius,then find the radius of the circle $DEF.$ This triangle is not given to be equilateral or anything else.Only the three ...
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1answer
47 views

Prove the general case of Common tangents

Prove the direct common tangent of 2 circles touching externally is the geometric mean of their diameters(meaning that the square of the tangent is the product of the diameters). Prove that the ...
3
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1answer
90 views

Find the maximum number of rational points on the circle with center $(0,\sqrt3)$

Find the maximum number of rational points on the circle with center $(0,\sqrt3)$ Let the equation of the circle be $x^2+(y-\sqrt3)^2=r^2$ Let $(a,b)$ be any rational point on the circle ...
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1answer
69 views

Line $x=-1$ is side BC of equilateral triangle ABC circumscribing circle $x^2 + y^2 = a^2$

An equilateral triangle ABC circumscribes the circle with equation $x^2 + y^2 = a^2$. The side BC of the triangle has equation $x = -a$. a) Find the equations of AB and AC. b) Find the equation of ...
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1answer
65 views

Using Radical Axis to prove Concurrence

Let $BB',CC'$ be altitudes in $\triangle ABC$, and assume $AB\neq AC$. Let $M$ be the midpoint of $BC$, $H$ the orthocenter of $\triangle ABC$, and define $D$ as the intersection of lines $BC$ and ...
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2answers
76 views

A circle centered at the origin is tangent to $y=2^x$. What is the radius of the circle?

I feel as though I am doing the analytical part correctly, however, where I am facing the roadblocks in this problem is in the actual algebra itself. Perhaps I am not doing something right in my ...
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1answer
19 views

degrees to radians conversion by multiplying into 360 degrees

I was just going though some fairly simple code and came across the following Math to translate degrees to radians, ...
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3answers
49 views

Finding the value of $k$ for the equation of a circle

I have been told that the circle with equation $x^2 + y^2 - 12x -10y + k=0$ meets the co-ordinate axes exactly three times, and I have to find the value of $k$. Now, I first found the centre of the ...
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0answers
18 views

The name of a polygon defined by multiple overlapping annuli

I am working on a problem in a metric space where points are partitioned into various annuli. If there exists multiple annuli that define a set of points then a polygon can be formed from their ...
2
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2answers
48 views

$AB$ is any chord of the circle $x^2+y^2-6x-8y-11=0,$which subtend $90^\circ$ at $(1,2)$.If locus of mid-point of $AB$ is circle $x^2+y^2-2ax-2by-c=0$

$AB$ is any chord of the circle $x^2+y^2-6x-8y-11=0,$which subtend $90^\circ$ at $(1,2)$.If locus of mid-point of $AB$ is circle $x^2+y^2-2ax-2by-c=0$.Find $a,b,c$. The point $(1,2)$ is inside the ...
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3answers
54 views

Real numbers $x,y$ satisfies $x^2+y^2=1.$If the minimum and maximum value of the expression $z=\frac{4-y}{7-x}$ are $m$ and $M$

Real numbers $x,y$ satisfies $x^2+y^2=1.$If the minimum and maximum value of the expression $z=\frac{4-y}{7-x}$ are $m$ and $M$ respectively,then find $2M+6m.$ Let $x=\cos\theta$ and ...
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1answer
25 views

Will the chord of a larger central angle be longer than the chord of a smaller central angle? [closed]

"In a circle, suppose we draw any central angle at all, then draw a second central angle which is larger than the first. Will the chord of the second central angle be longer than the chord of the ...
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4answers
242 views

What is the approximate area of the shaded region of the given figure?

How do i find the area of the black shaded portion of the circle? I noticed the 4 so i think that's the radius. The formula to find the area $$A=πr^2$$ so I thought of using that to find the area ...
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3answers
100 views

Displacement of a point on a circle

There is a mark on a wheel of radius $30$ cm. The mark is in contact with a horizontal plane. The wheel rotates to a distance of $10\pi \approx 31.4$ cm. $1.$ What is the angle that the old position ...
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1answer
32 views

Problem on comparision of radii

The radius of one circle is $4$ times that of a second. Compare an arc subtending $45°$ at the centre of the first with one subtending $60°$ at the centre of second. I understood the first part ...
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1answer
51 views

Finding suqares in the rectangle $(0,0,1,1)$ which are “divided with” $\frac{\pi}{4}$ by the unit circle.

I want to write an algorithm which calculates the following: Find all suqares $(x_0,y_0,x_1,y_1)$ which are "in" the suqare $(0,0,1,1)$ and are divided by the unit circle so that their inner area ...
3
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2answers
57 views

Find range of values for p in equation of circle

Can somebody please check my working with the following question: Given the equation ${x^2 + y^2 - 2px - 4py + 3p + 2 = 0}$ represents a circle, determine a range of values for p. I don't ...
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2answers
73 views

How to find the arc measure of the arc cut by one side the of a circumscribed regular polygon?

First, circumscribed means inside a circle, right? What does it exactly mean by cut by one side? A regular hexagon has side angles each $120 ^o$ so it has $240^o$ arc measure. But why is the answer ...
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2answers
43 views

Problem Based on Theorem of radius, arc length and central angle

An arc AB of a circle with radius 28 cm and center O subtends an angle AOB at the centre. If the length of arc AB is $$\frac{88}{3}$$ cm, find the length of chord AB. I haven't solve any question of ...
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5answers
236 views

find the equation of a circle from 3 points on circumference

The following question is from higher maths 2014 Scotland (a) Find P and Q, the points of intersection of the line ${y = 3x - 5}$ and the circle ${C_1}$ with the equation ${x^2 + y^2 + 2x - 4y ...
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1answer
64 views

Spherical circle - Area

I am looking at the following exercise: The spherical circle of centre $p \in S^2$ and radius $R$ is the set of points of $S^2$ that are a spherical distance $R$ from $p$. If $0 \leq R \leq ...
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0answers
23 views

Understanding calculation for half circle in canvas

I was just going through the source code of circliful.js and came across the following lines of code: ...
2
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1answer
30 views

circle radius from two points and the angle of one tangent with the horizontal axis

I want to find the radius $R$ knowing the coordinates of two points $(x_1,y_1)$ and $(x_2,y_2)$ the angle $\alpha$ between a tangent to the circle passing by $(x_1,y_1)$ and the horizontal Note ...
2
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1answer
86 views

Arclength between two points on a circle not knowing theta

What is the formula to calculate the distance (arc length) between 2 points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ on the circumference of a circle of radius $r$ without knowing the angle $\theta$ ...
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1answer
48 views

Finding equation of circle knowing 1 point, radius and that it touches the x-axis

I'm currently studying circle co-ordinate geometry, and this problem has puzzled me. Find the equations of the circles of radius $5$, which touch the x-axis, and pass through the point $(3,1)$. I ...
2
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1answer
208 views

Is it impossible to construct an equilateral triangle inside a semicircle?

I have made it in a circle(which is very easy)....but I have been unable to make one inside a semicircle....is it not possible to make equilateral triangle inside a semicircle ?... If yes how can we ...
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1answer
54 views

Circles are drawn through $P$ touching the coordinate axes,such that the length of the common chord of these circles is maximum.Find the ratio $a:b$

$P(a,b)$ is a point in the first quadrant.Circles are drawn through $P$ touching the coordinate axes,such that the length of the common chord of these circles is maximum.Find the ratio $a:b$. The ...
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1answer
47 views

Can circles drawn on a sphere (under specific conditions) intersect?

Gave the SAT exam recently and almost aced the Maths section. Almost because there was this one question I couldn't wrap my head around to solve. I don't remember the exact question, but it went ...
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2answers
25 views

Understanding Math formula that excludes a part of the circle

I just came across the below line of code , in javascript: additionalAngelPI = (90 / 180) * Math.PI; This is a Math question though , basically the above ...
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2answers
73 views

Proving result in inscribed triangles.

ABC is a triangle inscribed in a circle, and E is the mid-point of the arc subtended by BC different from the arc A on which A lies. If through E a diameter ED is drawn, show that $$\angle ...
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0answers
53 views

prove $x^{2n} + y^{2m} = 1$ is a “closed” shape

How do I show that $x^{2n} + y^{2m} = 1$ has a domain of $|x| \leq 1$? How would I show the opposite, that $$x^{2n-1} + y^{2m-1} = 1$$ has a domain covering all real values?
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1answer
51 views

Draw part of circle

I am trying to draw the following part of circle on a mobile screen but I can't do the math properly. Please, ignore the text. The left top corner is (0, 0) and the right bottom corner is (w, h). ...
3
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1answer
38 views

Differential Geometry: ODE question using parametrization of circle

Here is an example from the textbook which I need help with: Consider the equation $F(x, y) = x^2 + y^2 = c$. The gradient is given by $(2x, 2y)$ and only vanishes at the origin. The differential ...
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1answer
39 views

Proving in geometry, two circles cut.

$A$ is one of the points where the two circles are cut. $AB$ is a chord in the left circle and it's tangent in point A to the right circle. $AC$ is a chord in the right circle and it's tangent in ...
5
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2answers
73 views

Question on circle and equilateral triangles [duplicate]

Let $ABC$ be a triangle. Let $T$ be its circumcircle and let $I$ be its incenter. Let the internal bisectors of $A,B,C$ meet $T$ at $A',B',C'$ respectively. Let $B'C'$ intersect $AA'$ at $P$ and $AC$ ...
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1answer
60 views

Calculating the area of a triplet of circles.

I have an image of the problem which is quite self-explanatory. Any ideas?