Circulators
Four unit circles are inscribed inside a larger circle as shown on the figure provided. if the area of the red region is M and that of the green region is N , then :
= ?
The answer is 4.
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1 solution
The centres of the four unit circles form four vertices of a square of side-length 2 , and the diagonal of the square = 2√2 . The radius of the larger circle = (2√2 + 2)/2 = √2 + 1.
Af = area which is inside larger circle but out side the four unit circles = π { ( √2 + 1 ) ² - 4 } = 2√2π – π.
M = area of square – 4 quarter unit circles = 4 – π.
4N = Af - M = 2√2π – π – 4 + π = 2√2π – 4.
N = π/√2 -1.
N + 1 = π/√2.
Hence answer is 4 .