Disk covering problem $r(9)$

The smallest value $r(9)$ such that $9$ disks of radius $r(9)$ can be arranged to cover the unit disk.

Updates

• Upper bound: ${\approx}0.414213$
  Reference unknown
  [via Circles Covering Circles, Erich Friedman]
• 1996 Lower bound: ${\approx}0.414213$
  Gábor Fejes Tóth in 1996
  [via Circles Covering Circles, Erich Friedman]