# Tagged Questions

27 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 ...
34 views

### Geometry : find the points of tangency between two lines and two circles [on hold]

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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### 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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### Points of intersection between circle and parabola

Find the points of intersection between circle and a parable: circle: $x^2 + y^2 - 2x + 4y - 11 = 0$ parable: $y = (-x^2+ 2x + 1 - 2\sqrt{3})$ I don't understand how to solve this, I really tried, ...
20 views

### Area covered by multiple (possibly intersecting) circles on surface of sphere

I have a number of circles of same radius on surface of sphere (Google Maps API). I'm trying to calculate the total area covered by these possibly intersecting circles. My current solution is ...
37 views

### Finding the points of intersection of the circles [closed]

How can you find the points of intersection of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2+2x+2y-2=0$?
68 views

### Area of intersection between 4 overlapping circles.

I'm having difficulties finding the are of a section on the 4th circle when 4 circles intersect. The circles have a diameter of 150 mm, and the centers of adjacent circles are 100 mm apart. The shaded ...
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### Finding the area of the shaded region on a circle.

So I need help finding the area of the shaded A region. I was going to do pi*(r^2)*(45/360) - (the area of the smaller triangle). I just dont know how to get the angle or the lengths of it. Is there ...
39 views

### Two circles intersection

Could you tell what are all the four points in following? Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is ...
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### Two circle intersection

Two circles intersect at two points maximum when we want to draw intersecting circles. But there we are solving quadratic equations, what is the argument about the other two missing points?
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### Determine the closest point along a circle's $(x_1, y_1)$ radius from any point $(x_2, y_2)$, inside or outside the radius of the circle.

I have a circle centered at point $(x_1, y_1)$ and another point at $(x_2, y_2)$. This point, $(x_2, y_2)$ may or may not be within the radius ($r$) of the circle. I wanted to create a line going from ...
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### Is there a relation for when a circle intersects more than half the perimeter/circumference of another circle?

Is there some nice formula or algoritm for determining when a circle "hides"/intersects more than half of the perimeter of another circle, in a circle-circle interaction. Example image: Two example ...
46 views

### Crossing Circles

On a plane, you are only allowed to draw circles. After drawing 1 circle, can you ALWAYS draw another so that the new circle crosses all existing circles at 2 points? Why?
119 views

### Check whether $n$ disks intersect

I struggle with the following problem: Given $N$ disks $D_i = (x_i, y_i,r_i)$, calculate whether they ALL intersect. $D_1 \cap D_2 \cap \dots \cap D_N = \emptyset$ ? I do not care about the ...
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### Area of intersection between 4 circles?

Which is the area of the shown region? the radius in my case is 100m, thank you! Please try to make it easy. The centers of the cercle are placed in the vertex of square 100m of side.
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### stuck on a Cartesian question

we have a circle $(x-1)^2+(y-2)^2=9$ Point $P=(5,2)$ lies outside the circle. Solve the equation of the line which passes through $P$ and intersects the circle at two points whose mutual distance is ...
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### Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...
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### Is there an equation to find the intersection of 3 circles without complex steps?

Is there a way to find the intersection 3 circles without substituting and solving the equations into each other? The reason is because I am making a trilateration program, so I won't really be able ...
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### 3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
112 views

### Ray Disk intersection

So if I have a ray parameterized as $O + tD$ where $O$ is the origin, $D$ is the direction and $t$ is the parameter variable and a flat circular disk with a center point $P$ in 3D space and a radius ...
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### Determine the coordinate of the point where line and circle collide/intersect - how to solve for x

I would like to determine the point $C$ in this image: (assume I have radius value). After the hours of research and refreshing some memories from school days, I've got: Please assume... Point: ...
101 views

### How do I calculate a point on each of three circles that have specific distance to each other?

I am trying to write code for a computer simulator. I need to simulate a complex mechanism where each link has a known length and the ends of the links are connected to a triangle. I would like help ...
436 views

### Equation to determine radius for a circle that should intersect a given point?

Simple question. I tried Google but I don't know what search keywords to use. I have two points on a 2d plane. Point 1 = x1 and y1, and Point 2 = x2 and y2. I'd like to draw a circle around Point ...
15k views

### How can I find the points at which two circles intersect?

Given the radius and $x,y$ coordinates of the center point of two circles how can I calculate their points of intersection if they have any?
17k views

### How do I calculate the intersection(s) of a straight line and a circle?

The basic equation for a straight line is $y = mx + b$, where $b$ is the height of the line at $x = 0$ and $m$ is the gradient. The basic equation for a circle is $(x - c)^2 + (y - d)^2 = r^2$, where ...
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### Divide circle into 9 pieces of equal area

I'd like to divide a unit circle disk into nine parts of equal area, using circle arcs as delimiting lines. The whole setup should be symmetric under the symmetry group of the square, i.e. 4 mirror ...
188 views

### Angle of first circle where it intersects second circle

First, some background. I'm writing an application which a bit more mathematically challenging than what I'm used to. I have two circles that overlap (not just touch, I mean there are two intersect ...
96 views

### Find the intersection between point and circle

given a line segment with endpoints P1 and P2 and a Circle with Center C and Radius R where it is known that P1 lies outside the circle and P2 lies inside the circle, what is an efficient way to find ...
315 views

### How to find the intersection of union of two circle groups

I have two groups of circles. S1 is the union of the first group and S2 is the union of the second group of circles. I know center and radius of all circles. I have to find the equation for the ...
395 views

### Circular Sector to Circle Intersection

Is there a formula for determining if a sector intersects a circle (as well as determining if the circle/sector are inside each other)? Sector definition: A center point $P(x,y)$, a starting angle in ...
525 views

### 3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
426 views

### Position of 3 circles intersecting at the centre of bounding box

Here's what I feel is a neat challenge: I'm building a data visualization comprised of 3 circles of dynamic sizes. I want to have them all intersect at the centre of a bounding box that will also be ...
615 views

### How to check if circles intersect each other?

I'm trying to do trilateration where I know the coordinates of three known points and the estimates of the radii - not guaranteed to be really precise. My question is, how can I check if the circles ...