Answer:
AB = 7.35 cm
Step-by-step explanation:
From the attachment,
In ΔDEF,
DF = GH-(GD+FH) = 6 - (2+3) = 1 cm
DE = 2+3 = 5 cm (sum of two radius)
Applying Pythagoras theorem,
[tex]EF=\sqrt{DE^2-DF^2}=\sqrt{5^2-1^2}=\sqrt{24}=2\sqrt6[/tex]
In ΔCDI,
DI = GH-(GD+IH) = 6 - (2+1.5) = 2.5 cm
CD = 2+1.5 = 3.5 cm (sum of two radius)
Applying Pythagoras theorem,
[tex]CI=\sqrt{CD^2-DI^2}=\sqrt{3.5^2-2.5^2}=\sqrt6[/tex]
AB = EF + CI = [tex]2\sqrt6+\sqrt6=3\sqrt6=7.35\ cm[/tex]
