Disk covering problem $r(1)$

The smallest value $r(1)$ such that $1$ disks of radius $r(1)$ can be arranged to cover the unit disk.

Updates

• Lower bound: $1$
  Trivial or easy according to the secondary source.
  [via Circles Covering Circles, Erich Friedman]
• Upper bound: $1$
  Trivial or easy according to the secondary source.
  [via Circles Covering Circles, Erich Friedman]