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
141 views

Determining intersecting points between square and circle

I unfortunately have spent too much time trying to solve this question, and have turned to you for help. The corner of my square has intersected some circle, and I need to move it out. I only know one ...
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2answers
243 views

Geometry : find the points of tangency between two lines and two circles [closed]

I have a programming problem. I need to find the intersection points between two lines tangent to two circles and the circles! I have the circles' radiuses and centers. So I need points ...
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2answers
79 views

Find radius and height

I have the following problem: given the length of the chord AB and the length of the arc AB, find the radius of the circle and the height of the triangle ACB where C is a point on the circle such that ...
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1answer
108 views

How to embed this circle tangent to the other circles?

I want to construct a circle that would be tangent to the $3$ circles and would have its diameter lie somewhere on the segment $BI$. $EF$ includes the diameters of the $3$ given circles. $EB=BF$. ...
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3answers
132 views

The sum of the squares of the length of the chord intercepted by the line x+y=n $n$…

Problem : The sum of the squares of the length of the chord intercepted by the line x+y=n $n \in N$ on the circle $x^2+y^2=4$ is (a) 11 (b) 22 (c) 33 (d) 13 I am unable to understand this ...
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1answer
156 views

Best fit circular arc to an elliptical arc?

Is there a standard procedure or algorithm for finding the best fit circular arc to an elliptical arc ? Where the ellipse arc is: symmetrical about the minor axis, subtending $[+\theta, -\theta]$ ...
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2answers
40 views

If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ the…

Problem : If the circle $x^2+y^2+4x+22y+c=0$ bisects the circmuference of the circle $x^2+y^2-2x+8y-d=0$ then c +d equals (a) 60 (b) 50 (c) 40 (d) 30 Solution : Equation of common chord ...
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1answer
111 views

Circle with perpendicular chords

A blue circle is divided into $100$ arcs by $100$ red points such that the lengths of the arcs are the positive integers from $1$ to $100$ in an arbitrary order. Prove that there exists two ...
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2answers
253 views

Area of a segment

Two circles of radii 5cm and 12cm are drawn, partly overlapping as shown. Their centres are 13cm apart. Find the area common to the circles?
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1answer
1k views

Parametric equation of a circle given starting point.

Find the parametric equations of a circle with radius of $5$ where you start at point $(5,0)$ at $v=0$ and you travel clockwise with a period of $3$. So, I know that I require to have a $x(v)$ and $y(...
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1answer
124 views

Diameter of inscribed circle

How can i express diameter of inscribed circle in terms of radius of three circles.
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2answers
108 views

Do the centers of mass of the whole $n$-sphere and its half coincide when $n \to \infty$?

It is known that the distance between the centroid (center of mass) and the center of a unit semicircle is $\displaystyle\frac{4}{3\pi}$, whereas that of a unit hemisphere is $\displaystyle\frac{3}{8}$...
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1answer
54 views

If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P…

Problem : If the distances from origin of centre of three circles $x^2+y^2+2\lambda_i-c^2=0$ (i=1,2,3) are in G.P ( Geometric progression). Then lengths of tangents drawn to them from any point on the ...
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2answers
47 views

Find the radius

Consider the parabola $y=x^2$ and a circle which is tangent to the parabola at the points $(1,1)$ and $(-1,1)$.Find the radius of circle. My try:I write the general equation of circle $(x-h)^2+(y-k)...
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1answer
129 views

Inverted Circle?

The equation I have is $$\Large x^{\frac23} + y^{\frac23} = 3^{\frac23} $$ I know what the graph looks like, but I don't know how I would find points other than the intercepts mathematically. How ...
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1answer
236 views

The point of contact between a line with a circle

My question is: I have a circle of radius 40 and a line which the circle is tangent to. So, if I take a circle of radius 80, do the two circles have the same point of contact? I mean: do they (my ...
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5answers
286 views

How to work out miles between Longitude values based on a Latitude value.

We know that when Latitude is 0, the distance between Longitude values is roughly 69 miles. When the Latitude is +/-90, Longitude values are 0 miles. At 0 Latitude, the earths circumference is 24,...
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0answers
58 views

Find angle of an arc in the circle using 3 coordinates

I want to find angle of semicircle. I have 3 coordinates (center_a,center_b) , (pivot_a,pivot_b) and (last_point_a, last_point_b). From triangle , i can find angle using equation using cosine ...
2
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1answer
73 views

Line not intersecting circle, maximum value of expression involving radius

If line $y+x=2$ do not intersect any member of circles $x^2 + y^2 -ax = 0$ at two distinct points where a is parameter, then maximum value of $|a + 4|$. My try: Since the line does not intersect ...
4
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2answers
738 views

The area of circle

The question is to prove that area of a circle with radius $r$ is $\pi r^2$ using integral. I tried to write $$A=\int\limits_{-r}^{r}2\sqrt{r^2-x^2}\ dx$$ but I don't know what to do next.
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2answers
179 views

Calculate the closest point to the center of a circle from another circle on its radius.

There are 2 circles, the smaller one has its center on the bigger circles border, from that how can you calculate the coordinates the closest point on the smaller circle to the center of the bigger ...
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4answers
5k views

Area of a Circle Inscribed in a Square

A circle is inscribed in a square. The diameter of the circle is 12.4 mm. Find the area of the region that is outside of the circle and inside the square. Round the answer to the nearest tenth.
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0answers
56 views

Rotation of point with infinite child objects. (Chain rotation)

More of a thought experiment here, knowledge for knowledges sake. Let's say you can create infinite points that rotate smoothly and at the same speed as each other through a full revolution - let's ...
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0answers
129 views

Packing circles in circle vs semicircle vs quarter of circle

Consider $N$ disjoint circles with radius $1$ packed into a larger circle $C$. Let $R$ be the smallest possible radius of $C$, allowing the best packing density. Now take the $N$ unitary circles ...
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1answer
57 views

Radius of a circle

I'm having trouble with a question where I'm given two points, (-5,-2) & (1,0). Find the equation of the circle. I've used the midpoint formula to get the center which is (x+2) & (y+1) If I'm ...
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2answers
130 views

internal rectangle area intersected by a circle

I need to compute the internal rectangle area intersected by a circle like (the blue area) on these 3 examples: I know every vertex (x,y) coordinate and then their distance from circle center but ...
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17answers
5k views

How to create circles and or sections of a circle when the centre is inaccessible

I am doing landscaping and some times I need to create circles or parts of circles that would put the centre of the circle in the neighbours' garden, or there are other obstructions that stop me from ...
2
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1answer
51 views

Calculating a specific point on a circle

I am looking for a formula to calculate the point of intersection where the arc crosses the angled line (designated by the letter 'X' in the example below), only from the dimensions given. I am ...
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1answer
45 views

Circles and tangents

3 circles of radius 3 cm, 4cm, 5 cm touch each other externally at $A$, $B$, $C$. Tangents drawn at $A$, $B$, $C$ intersect at $P$. Find $ PA + PB + PC$ . Thanks. My thoughts and approach: ...
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2answers
141 views

Proof when the circle map is ergodic

Let $E=[0,1)$ with Lebesgue measure. For $a \in E$ consider the mapping $\theta_a:E \rightarrow E, \ \ \theta_a(x) = (x+a) \mod \ 1$. a) Show that $\theta_a$ is not ergodic when $a$ is rational. ...
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1answer
270 views

What proportion of the circle is covered by the square?

Or what is the combined area of the circle segments (chords)? Picture a circle which is covered by a square, where the bottom vertices of the square are inscribed within the circle (so that the ...
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2answers
49 views

Locating a point on a circle

I am having trouble getting the $(x,y)$ of a certain point on the circle. Please look at the image: The circles are the identical, the radius is $1000 \text{ units}$, $S$ is the center with ...
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1answer
44 views

Area of an ellipse proportional to integral of cross-ellipse distances?

I am curious if the area of an ellipse can be shown to be proportional to the integral of all cross-ellipse distances. Before I define cross-ellipse distance, I will give a motivating example from a ...
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2answers
69 views

How to find angular distance between points? [duplicate]

I have the following problem. I have several points on the plain, and there is another point somewhere in the middle of them. The goal is to find angular distance between any two points. My only ...
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3answers
1k views

How can I find the smallest enclosing circle for a rectangle?

I have the four vertices of a rectangle. I need to find it's smallest enclosing circle. For example: I need to find the radius of the circle.
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4answers
233 views

Showing that a circle is “tangent” to the $x$-axis if and only if $\left|k\right| = r$.

The problem is this: to show that a circle of radius $r$ and center $(h, k)$ intersects the $x$-axis at exactly one point if and only if $\left|k\right| = r$. Using geometrical intuition, this ...
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1answer
260 views

Find if a point lies in all given circles

I have a set of n given circles. I want to find that if there exists at least one point that lies in all of the given circles. Is there a method to do so? I can ...
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2answers
2k views

Prove that two circles are congruent if their radii are equal

Is this to be proved by showing that the circumferences/areas are equal?
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4answers
177 views

Find the equation of a circle which is tangent to $y$-axis at a given point and cuts a chord of given length on the $x$-axis

How to find the equation of the circle which touches $y$ axis at $(0,3)$ and cuts a chord of length $8$ on the $x$ axis? It should look like this: My approach: Since the circle touches $y$ ...
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2answers
75 views

Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
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3answers
972 views

Diameter of a circle using 3 nonlinear points

I am trying to find the diameter of a circle using 3 points on its circumference. 2 of the points are 5 feet from eachother while the third point is centered between the other 2. The ceter point is ...
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1answer
436 views

The surface area of a ring: $\pi[(r+dr)^2 - r^2]$ or $2\pi r\,dr$?

I know this may be really simple but here it is nonetheless. Let's say that I have a ring with a radius of $r$ and width of $dr$. I'm trying to find the surface $dS$ of the ring. Isn't it $dS = \pi[(r+...
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2answers
331 views

Rotation number of inverse maps on the circle.

I'm still a bit lost in my studies of rotation numbers. Any help is much appreciated! Let's say we have a homeomorphism $F: \mathbb{R} \rightarrow \mathbb{R}$ which is a lift of a homeomorphism $f:S^...
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2answers
119 views

Locus of vertex of triangle moving inside circle

A right triangle with sides $3,4$ and $5$ lies inside the circle $2x^2+2y^2=25$. The triangle is moved inside the circle in such a way that its hypotenuse always forms a chord of the circle. The locus ...
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4answers
1k views

True or False: The circumradius of a triangle is twice its inradius if and only if the triangle is equilateral.

Let $R$ be the circumradius and $r$ be the inradius. The if part is clear to me. For an equilateral triangle, the circumcentre, the incentre and the centroid are the same point. So, by property of ...
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7answers
878 views

Finding all the values of $\theta$ for which $\tan(\theta)=\sqrt3$; problem with understanding.

My textbook has a section where it says a possible way that $\tan(\theta)$ can be thought of is: For acute angles $\theta$, $\tan(\theta)$ is the $y$-coordinate of the point on the terminal side ...
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1answer
908 views

The locus of centre of circle tangent to two given circles

What is the locus of the centre of circles that are tangent to two given circles? I had no idea how to approach the problem so I considered a special case, namely one in which the two circles were ...
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1answer
693 views

finding points with maximum distance between them on a circle

I'm a computer science student working on a problem in computer graphics and looking for a formula that can find the x and y positions of a set of N points on the surface of a circle so that the ...
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3answers
155 views

Please find the radius of the circle.

Hello, I want to find the radius of red circle. I tried it with several ways like trigonometric. But there is a special value is given with this. I can not understand why it is given. It is the blue ...
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2answers
200 views

A question about 4 concyclic points

In a triangle $ABC$, let $I$ denote its incenter. Points $D, E, F$ are chosen on the segments $BC, CA, AB$, respectively, such that $BD + BF = AC$ and $CD + CE = AB$. The circumcircles of triangles $...