Let the radius of the smallest circle be r = 4 cm.
The area of the smallest circle is given by A = πr^2 = 16π cm^2.
Let the radius of the nth circle be R.
The area of the nth circle is given by A_n = πR^2.
According to the given conditions, the area of each consecutive circle is 9/4 times that of the previous circle. Therefore:
A_2 = 9/4 * A = 9/4 * 16π = 36π
A_3 = 9/4 * A_2 = 9/4 * 36π = 81π
A_4 = 9/4 * A_3 = 9/4 * 81π = 182.25π
The distance from AB = 665/8 is the distance from the centre of each circle. We can use this information to find the radius of the largest circle.
Let the radius of the largest circle be R_max. The distance from the center to AB is R_max - r, the sum of radii of all previous circles.
R_max - r = 665/8
R_max = r + 665/8 = 4 + 665/8 = 537/8 cm
Let N be the number of circles.
As the circles are touching each other, the sum of their radii should be equal to the total distance between AB.
r + R + R + ... + R_max = 537/8
N*R = 537/8 - 4
N* 537/8 = 537/8 - 32/8
N*537 = 505/8
N = 505/8 * 8/537
N = 505/537
N = 5
Therefore, there are 5 circles arranged such that the smallest circle has a radius of 4 cm and each consecutive circle has an area 9/4 times that of the previous circle.
Number of circles touch each other the smallest circle is 4cm and each consecutive circle has an area 9/4times that of the previous zone of the distance from AB =665/8 line AB passes at the centre of the circles how man circles are there
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