Do the circles overlap?

Question

Given the coordinates of the centres and the radii of 2 circles, output a truthy value of whether they do or do not overlap.

Input

• Input may be taken via STDIN or equivalent, function arguments, but not as a variable. You can take them as a single variable (list, string etc) or as multiple inputs / arguments, in whatever order you want.

• The input will be six floats. These floats will be up to 3 decimal places. The coordinates can be positive or negative. The radii will be positive.

Output

• Output can be via STDOUT or function return.

• The program must have exactly 2 distinct outputs - one for a True value (the circles do overlap) and one for a False output (they don't overlap).

Test cases

(Input is given as list of tuples [(x1, y1, r1), (x2, y2, r2)] for the test cases; you can take input in any format)

True

[(5.86, 3.92, 1.670), (11.8, 2.98, 4.571)]
[(8.26, -2.72, 2.488), (4.59, -2.97, 1.345)]
[(9.32, -7.77, 2.8), (6.21, -8.51, 0.4)]

False

[(4.59, -2.97, 1.345), (11.8, 2.98, 4.571)]
[(9.32, -7.77, 2.8), (4.59, -2.97, 1.345)]
[(5.86, 3.92, 1.670), (6.21, -8.51, 0.4)]

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This is Code Golf, shortest answer in bytes wins.

Answer 1

Go, 93 bytes

package q
import c "math/cmplx"
func o(a,b complex128,r,R float64)bool{return c.Abs(b-a)<r+R}

Fairly simple algorithm, same as several other answers, except it uses the built-in complex type and calls math/cmplx.Abs().

Taking the radii as complex numbers doesn't help, because the cast to float64 adds more bytes than the variable declaration saves (can't do float64 < complex128).

Try it online! Includes the test cases, and uses package main instead of a library.

Answer 2

Javascript, 38 chars

(x,y,r,X,Y,R)=>Math.hypot(X-x,Y-y)<R+r

Test:

f=(x,y,r,X,Y,R)=>Math.hypot(X-x,Y-y)<R+r

console.log(
  f(5.86, 3.92, 1.670, 11.8, 2.98, 4.571),
  f(8.26, -2.72, 2.488, 4.59, -2.97, 1.345),
  f(9.32, -7.77, 2.8, 6.21, -8.51, 0.4)
);

console.log(
  f(4.59, -2.97, 1.345, 11.8, 2.98, 4.571),
  f(9.32, -7.77, 2.8, 4.59, -2.97, 1.345),
  f(5.86, 3.92, 1.670, 6.21, -8.51, 0.4)
);

Answer 3

QBIC, 30 bytes

?abs(:-:)^2+abs(:-:)^2<(:+:)^2

Basically does a²+b²=c². Takes parameters in the order of x1, x2, y1, y2, r1, r2.

                 The code builds a triangle y doing a²+b²=c²
?abs(:-:)^2      Takes the size of our triangle along the x-axis
+abs(:-:)^2      Takes the size of our triangle along the y-axis
 (:+:)^2         Takes the length of both radii
<                And compares them. The circles overlap (-1) if their combined 
                 radii is bigger than the c-side of the triangle

Answer 4

Swift, 47 Bytes

($0-$3)*($0-$3)+($1-$4)*($1-$4)<($2+$5)*($2+$5)

$0, $1, ... are implicit closure parameters. To use, assign to a variable with a type annotation:

let f: (
    _ x1: Double, // $0 ----+
    _ y1: Double, // $1 ----|----+
    _ r1: Double, // $2 ----|----|----+
    _ x2: Double, // $3 ----+    |    |
    _ y2: Double, // $4 ---------+    |
    _ r2: Double  // $5 --------------+
    ) -> Bool = {
     ($0-$3)*($0-$3)+($1-$4)*($1-$4)<($2+$5)*($2+$5)
}

Answer 5

Perl 5, 54 bytes

$_=$F[2]+$F[5]>sqrt(($F[0]-$F[3])**2+($F[1]-$F[4])**2)

Try it online!

Input format:

x1 y1 r1 x2 y2 r2