Little Chandler is sad. Draw him a cloud to cheer him up
T-SQL 235 234 229 212 171 73 bytes
This makes use of spatial functionality in SQL Server 2012+.  When it is run in SSMS (SQL Server Management Studio) is produces a spatial results pane.
The input is from variable @i.  I could reduce it further if the input could be taken from a table.
Since table input is now allowed.
SELECT Geometry::UnionAggregate(Geometry::Point(X,Y,0).STBuffer(R))FROM A

I've left the previous solution below.
DECLARE @ VARCHAR(999)='WITH a AS(SELECT *FROM(VALUES('+REPLACE(@i,' ','),(')+'))A(X,Y,R))SELECT Geometry::UnionAggregate(Geometry::Point(X,Y,0).STBuffer(R))FROM a'EXEC(@)

Edit: Remove stray space, surplus into and subquery
171: Replaced table creation with CTE and @s with @.

Break down of the Dynamic SQL
DECLARE @i VARCHAR(100) = '1,4,2 5,2,1 3,1,1 3.5,2,1.2 3,3,0.7 1,2,0.7' -- Input
DECLARE @ VARCHAR(999) = '
WITH a AS(                                       --CTE to produce rows of x,y,r 
    SELECT *FROM(VALUES('+
        REPLACE(@i,' ','),(')                    --Format @i to a value set
        +'))A(X,Y,R)
)
SELECT Geometry::UnionAggregate(                 --Aggregate Buffered Points
    Geometry::Point(X,Y,0).STBuffer(R)           --Create point and buffer
    )               
FROM a                                           --from the table variable
'
EXEC(@)                                          --Execute Dynamic sql