Question

What is the relationship between R and r

Answer 1

R is radius of large circle and
r is radius of small circle

Answer 2

Concept:

The smaller circle's area is less then 1/4th time the area of the bigger circle as observed.

Given:

The larger circle's radius is 'R'.

The smaller circle's radius is 'r'.

The smaller circle is inside the bigger circle.

The smaller circle's area is less then 1/4th time the area of the bigger circle.

Find:

The relationship between the Radii of the bigger circle "R" and of the smaller circle "r".

Solution:

The area of the bigger circle will be πR²

The area of the smaller circle will be πr²

As the area of the smaller circle is less then 1/4th time the area of the bigger circle, then

area of the smaller circle < (1/4) ( area of the bigger circle )

πr² < (1/4) πR²

r² < (1/4) R²

taking square root both side

r < (1/2) R

r < R/2

Hence, the radius of the smaller circle "r" is less than half of the radius of the bigger circle.

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