Let r and R be the radii of the smaller circle and bigger circle respectively. ∴πR2=9×πr2⇒
R2
r2
=9⇒
R
r
=3 Now,ΔOAP ~ ΔAO'AQ ∴
AO′
AO
=
R
r
⇒
AO+r+R
AO
=3 ⇒AO+r+3r=3AO ⇒4r=2AO ⇒
r
AO
=
1
2
In right ΔOAP, sinθ=
r
AO
=
1
2
⇒ θ = 30° Remember: If two tangents are drawn to a circle from an externalpoint, then tangents are equally inclined to the segment joining the centre to that point. ∴ ∠A=2×30°=60°