SOLUTION TO GEOMETRICAL PUZZLE OF JUNE 1

We have,

Area of circle with radius R = πR²

and

Area of circle with radius r = πr²

First consider ΔABC where

AB² + BC² = AC²

∴ AB² + BC² = (2R)²

∴ AB² + BC² = 4R²

∴ AB² + AB² = 4R² (because AB = BC)

∴ AB² = 2R²

∴ MN² = 2R²

∴ (2r)² = 2R²

∴ 4r² = 2R²

∴ R² = 2r²

Now, πR² = 200

∴ π(2r²) = 200

∴ πr² = 100

Thus, the area of the smaller circle will be 100 sq. cm.

NOTE : I had received one anonymous comment with true answer. I would like to thank the HIDDEN IDENTITY.