# Tagged Questions

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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### 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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### 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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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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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### 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 ...
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### 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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### 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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### 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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### 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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### 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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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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### 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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### 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 ...
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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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 ...
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 \$...