AD is;
√(8²+3²-2*8*3cos60)
= √(73-24)
= √(49)
= 7 unit.
Therefore radius of area S1 is;
3r+7r+8r=12√(3)
r = (12√(3))/18
r = ⅔(√(3)) unit.
Area S2 = π(⅔(√(3)))²
= ⅓(4π) square unit.
Therefore radius of area S2 is;
5r+7r+8r=20√(3)
r = (20√(3))/20
r = √(3) unit.
Area S1 = π(√(3))²
= 3π square unit.
It implies;
S1 ÷ S2 is;
⅓(4π) ÷ 3π
= 4π ÷ 9π
= 4/9
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