The radius, r if the small circle will be;
(5+r)²=2(5-r)²
25+10r+r²=50-20r+2r²
Therefore
r²-30r+25=0
(r-15)²=-25+225
r = 15±√(200)
r = 15±10√(2)
It implies;
r ≠ 15+10√(2)
r = 15-10√(2) unit.
Therefore area blue will be;
¼(100-25π) - (15-10√(2))²π
= 3.05304958693 square unit.
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