How To Alter Table Drop Constraint @variable?

I need to run the alter table to drop a default. However, the default name is kind of 'dynamic' from around 1000 databases, thus I need to run the following sql to get the name to a variable. Now, it looks the alter table statement does not like to drop a vaiable, is there a solution about it?

declare @radius_default varchar(40)
select @radius_default = (select sobj.name from sysobjects sobj
inner join syscolumns scolumn
on sobj.ID = scolumn.cdefault
where scolumn.name = 'radius' and sobj.name like '%LandMarks%')
print 'Need To Drop @radius_default: ' + @radius_default
--====================================
alter table LandMarks drop constraint @radius_default

thanks
David