Sir Mike Ambrose is the author of the question.
Let r be the radius of the three congruent circles.
Calculating r.
(9+r)² = (9-r)²+(9-3r)²
81+18r+r² = 81-18r+r²+81-54r+9r²
36r = 81-54r+9r²
9r²-90r+81 = 0
r²-10r+9 = 0
r ≠ 9 units.
r = 1 unit.
a² = (2*9²)
a = 9√(2) units.
b² = 2(1)²
b = √(2) units.
c = a-b
c = 8√(2) units.
(8√(2))² = 10²+2²-2*2*10cosd
128 = 104-40cosd
cosd = (104-128)/40
d = 126.86989764584°
(8√(2)/sin126.86989764584) = (2/sine)
e = 8.13010235416°
f = 180-d-e
f = 45°
Therefore;
A Area to 2 decimal places square cm is;
2(0.5*8√(2)*2sin45 - ⅛(π) - 126.86989764584π/360 - 8.13010235416π*81/360)
= 2(8-0.3926990817-1.10714871779-5.74683071147)
= 2(0.75332148904)
= 1.50664297808 cm²
≈ 1.51 cm²
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