1
vote
1answer
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 ...
1
vote
2answers
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 ...
1
vote
2answers
33 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 ...
3
votes
1answer
40 views

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, ...
0
votes
0answers
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 ...
0
votes
1answer
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 $x^2+y^2+2x+2y-2=0$?
1
vote
1answer
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 ...
1
vote
2answers
68 views

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 ...
1
vote
1answer
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 ...
3
votes
1answer
60 views

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?
0
votes
1answer
47 views

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 ...
1
vote
0answers
44 views

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 ...
1
vote
1answer
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?
6
votes
4answers
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 ...
7
votes
4answers
222 views

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.
1
vote
1answer
39 views

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 ...
1
vote
1answer
60 views

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 ...
1
vote
1answer
1k views

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 ...
1
vote
1answer
258 views

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 ...
0
votes
1answer
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 ...
0
votes
2answers
412 views

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: ...
1
vote
2answers
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 ...
1
vote
3answers
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 ...
7
votes
4answers
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?
7
votes
3answers
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 ...
20
votes
2answers
2k views

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 ...
2
votes
1answer
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 ...
0
votes
1answer
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 ...
0
votes
1answer
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 ...
0
votes
1answer
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 ...
1
vote
1answer
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? ...
0
votes
2answers
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 ...
2
votes
1answer
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 ...
1
vote
3answers
7k views

Determine coordinate of intersection between a line and a circle

I'm putting together a simple script in processing to visualise layout possibilities within the fluid environment of a web page. I need some help calculating a point on a circle: The circle is as ...
2
votes
2answers
632 views

subvolume area under the intersection of a plane (line) and a cone

I am implementing a conical filter for Gupta-Sproull anti-aliased line algorithm. Given a cone with the total volume of 1 and a radius of 1. Find the subvolume of the intersection of a line. The ...