# Problem of Apollonius

```ruby
class Circle(x,y,r) {
    method to_s { "Circle(#{x}, #{y}, #{r})" }
}
 
func solve_apollonius(c, s) {
 
    var(c1, c2, c3) = c...
    var(s1, s2, s3) = s...
 
    var 𝑣11 = (2*c2.x - 2*c1.x)
    var 𝑣12 = (2*c2.y - 2*c1.y)
    var 𝑣13 = (c1.x**2 - c2.x**2 + c1.y**2 - c2.y**2 - c1.r**2 + c2.r**2)
    var 𝑣14 = (2*s2*c2.r - 2*s1*c1.r)
 
    var 𝑣21 = (2*c3.x - 2*c2.x)
    var 𝑣22 = (2*c3.y - 2*c2.y)
    var 𝑣23 = (c2.x**2 - c3.x**2 + c2.y**2 - c3.y**2 - c2.r**2 + c3.r**2)
    var 𝑣24 = (2*s3*c3.r - 2*s2*c2.r)
 
    var 𝑤12 = (𝑣12 / 𝑣11)
    var 𝑤13 = (𝑣13 / 𝑣11)
    var 𝑤14 = (𝑣14 / 𝑣11)
 
    var 𝑤22 = (𝑣22/𝑣21 - 𝑤12)
    var 𝑤23 = (𝑣23/𝑣21 - 𝑤13)
    var 𝑤24 = (𝑣24/𝑣21 - 𝑤14)
 
    var 𝑃 = (-𝑤23 / 𝑤22)
    var 𝑄 = (𝑤24 / 𝑤22)
    var 𝑀 = (-𝑤12*𝑃 - 𝑤13)
    var 𝑁 = (𝑤14 - 𝑤12*𝑄)
 
    var 𝑎 = (𝑁**2 + 𝑄**2 - 1)
    var 𝑏 = (2*𝑀*𝑁 - 2*𝑁*c1.x + 2*𝑃*𝑄 - 2*𝑄*c1.y + 2*s1*c1.r)
    var 𝑐 = (c1.x**2 + 𝑀**2 - 2*𝑀*c1.x + 𝑃**2 + c1.y**2 - 2*𝑃*c1.y - c1.r**2)
 
    var 𝐷 = (𝑏**2 - 4*𝑎*𝑐)
    var rs = ((-𝑏 - 𝐷.sqrt) / 2*𝑎)
 
    var xs = (𝑀 + 𝑁*rs)
    var ys = (𝑃 + 𝑄*rs)
 
    Circle(xs, ys, rs)
}
 
var c = [Circle(0, 0, 1), Circle(4, 0, 1), Circle(2, 4, 2)]
say solve_apollonius(c, %n<1 1 1>)
say solve_apollonius(c, %n<-1 -1 -1>)
```

#### Output:

```
Circle(2, 2.1, 3.9)
Circle(2, 0.83333333333333333333333333333333333333325, 1.166666666666666666666666666666666666667)
```


---

# Agent Instructions: Querying This Documentation

If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter:

```
GET https://trizen.gitbook.io/sidef-lang/programming_tasks/p/problem_of_apollonius.md?ask=<question>
```

The question should be specific, self-contained, and written in natural language.
The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.