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### How to calculate the intersection of 2 circles? [duplicate]

I am working on making inverse kinematics for a game I am making so I decided that the best way to start would be to do it in 2D. After asking some people how to do it, they said you need to ...
478 views

### How do you find the intersection(s) of two circles with equal radii? [duplicate]

I have two circles with the following equations: \begin{equation*} (x-a_1)^2+(y-b_1)^2=r^2 \\ (x-a_2)^2+(y-b_2)^2=r^2 \end{equation*} The two radii are equal. How do you find the intersections of any ...
277 views

### Find the coordinates of the points where the two circles intersect. [duplicate]

The two circles are: 1) $$(x-2)^2 + (y+1)^2 = 25$$ 2) $$(y-2)^2 + (x+1)^2 = 25$$
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### I want to write an algorithm for two circles intersection and touching cases . How can I do it with a quadtratic equation? [duplicate]

Given that two circles with coordinates (x1, y1) and (x2, y2) and radius r1 and r2 respectively . I need to find an equation , which can be used in code to to find the coordinates and the presence of ...
16k views

### Get location of vector/circle intersection?

I'm a coding guru, and I'm good with math - but only math that I know. Which isn't even at calculus level yet. So I'm hoping I can get some help here for my algorithm. Say I have a circle. I know its ...
5k views

### How can I calculate a point's coordinates given distances from three other known points? [duplicate]

I have a trilateration-related problem that I'm unsure how to solve mathematically. I can see a solution is possible through geometry, but I'm unsure how to solve the resulting equations. Given ...
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### Math and equations for external tangent lines between two dissimilar circles?

I am trying to determine the maths behind drawing a line from the top of one circle to the top of another (and bottom to bottom). I am doing this for a programmatically generated CAD file, I currently ...
754 views

### calculate points coordinates on plane from their distances matrix

Given a list of points on a plane is simple to generate a distances list between each pair of points. Pseudo Code: ...
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### Determine third point of triangle when two points and all sides are known

I am solving basically the same problem as asked in this thread Determine third point of triangle when two points and all sides are known? I know 3 sides of a triangle and positions of two of them. ...
723 views

### Circle-Cirle Intersection

Sorry for asking a question like this (can't comment as my reputation is too low). Could someone please explain this answer to me? Particularly the part, where the orthogonal vectors are declared? Why ...
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### intersection points of two circles

I am trying to find the points at which two circles intersect. The circles I am working with are: $$(1) \qquad x^2+y^2 = \frac{9}{4}$$ $$(2) \qquad (x-2)^2+y^2=\frac9 4$$ I am following this answer: ...
371 views

### Computing coordinates of vertices in a SSS triangle

Given that we know the lengths of the sides of a triangle (SSS), how can the coordinates of the vertices in the Euclidean plane of such a triangle be mathematically computed? I'm especially looking ...
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### Given the ratios of distances from three corners of a rectangle, find the coordinates of a point with said ratios.

I think the picture can explain it better than words, but I'm wondering how to figure this out. Given three ratios of distances from corners, not lengths (in the picture I set the base, $base=1$, to ...
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### intersection of 4 circles

Hi I'm doing some programming challenges for fun and I am trying to work out the maths required to solve this problem. It has been 10 years since I did any maths in anger like this so i'm a bit rusty....
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### Algebra steps breakdown

I have been reviewing this question. : How can I find the points at which two circles intersect? Although during the answering steps I got a little stuck: From this: 17y2−62y+49=0 To this: y=(31+...

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