Examine the figure and compare the Red and the Blue areas?
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Considering area of circle of radius 10
A 1 = B + W 1 + W 2
π ( 1 0 ) 2 = B + W 1 + W 2
Considering area of circle of radius 6
A 2 = R 2 + W 2
π ( 6 ) 2 = R 2 + W 2
Considering area of circle of radius 8
A 3 = R 1 + W 1
π ( 8 ) 2 = R 1 + W 1
Now,
6 2 + 8 2 = 1 0 2
π ( 6 ) 2 + π ( 8 ) 2 = π ( 1 0 ) 2
( R 2 + W 2 ) + ( R 1 + W 1 ) = B + W 1 + W 2
R 1 + R 2 = B
As R 1 + R 2 = R
Therefore, R = B
Thank you, Nice solution
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A r e a o f B l u e i s : 1 0 π 2 − Area of White
A r e a o f R e d I s : ( 6 π 2 + 4 π 2 ) − Area of White
Thus, Red = Blue