Draw 3 identical circles have centers A, B and C resp. with radius as r
Now, on joining all 3 centers, we will get an equilateral triangle with each side 2r

Height of this equilateral triangle = \(\frac{\sqrt{3}(side)}{2}\) = \(\frac{\sqrt{3}(2r)}{2}\) = \(\sqrt{3}r\)

Now, Join all 3 vertices (A, B and C) to the Centroid of this triangle.
You will notice, that the radius of bigger circle (let's say R) is \(\frac{2}{3}^{rd}\) the distance of Height of this equilateral triangle.

i.e R = \(\frac{2}{3}H\)
R = \(\frac{2}{3}\) x \(\sqrt{3}r\) = \(\frac{2r}{\sqrt{3}}\)

Percent Change = \(\frac{Difference}{Initial}\) x 100
= \(\frac{2r - \sqrt{3}r}{r}/r\)x 100
= \(\frac{2 - \sqrt{3}}{\sqrt{3}}\) x 100
= 15.47%

Hence, option A