The sum of circumference of four small circles is equal to the circumference of a bigger circle. find the rati

The sum of circumference of four small circles is equal to the circumference of a bigger circle. find the ratio of the area of the bigger circle to that of the smaller circle.

can anyone solve this question by full explanation ..... plz solve it soon

Radius of one small circle = r
Circumference of one small cirle = 2πr
Sum of circumferences of 4 small circles = 4*2πr = 8πr
Radius of the big circle = R
Circumference of the big circle = 2πR
As per the question : 2πR = 8πr , => R/r = 4/1
Area of the Big circle = A = πR²
Area of the small cirle = a = πr²
Hence , A/a = R² / r² = (R/r)² = (4/1)² = 16 / 1

C = circuference
R = radius

C = 2 pi R
R = C / 2pi

the sum of the radii of the 4 small circles is alos equalt to the radius of the big circle
Area = pi* R^2
if R increases by a factor of 4, thenm area increases by a facotr or 4^2 = 16

16 times the area of the small circles

let the radii of small 4 circles be r1,r2,r3,r4 and of bigger circle be R;
so 2 pi(r1 + r2 +r3 +r4)= 2 pi(R)
=> r1+r2+r3+r4=R....(1)

ratio of area of bigger circle to smaller ones = pi(R^2)/pi(r1^2 + r2^2 + r3^2 + r4^2)
=R^2/r1^2 + r2^2 + r3^2 + r4^2

=(r1+r2+r3+r4)^2) / (r1^2 + r2^2 + r3^2 + r4^2)
=(ri + r2)^2 +(r3+r4)^2 + 2(r1+r2)(r3+r4)/(r1^2 + r2^2 + r3^2 + r4^2)
=r1^2 + r2^2 + r3^2 + r4^2 + 2r1 r2 + 2r3 r4 + 2r1 r3 + 2r1 r4 + 2r2 r3 + 2r2 r4 / (r1^2 + r2^2 + r3^2 + r4^2)
=1 + (2(r1 r2 + r3 r4 + r1 r3 + r1 r4 + r2 r3 + r2 r4)/(r1^2 + r2^2 + r3^2 + r4^2))

That's it..I cant solve further!

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