Disk covering problem $r(2)$

The smallest value $r(2)$ such that $2$ disks of radius $r(2)$ can be arranged to cover the unit disk.

Updates

• Lower bound: $1$
  Trivial or easy according to the secondary source.
  [via Disk covering problem - Wikipedia]
• Upper bound: $1$
  Trivial or easy according to the secondary source.
  [via Disk covering problem - Wikipedia]