Nested mid-point squares inside a square and an inscribed circle:\nABCD is a square. EFGH is formed by joining midpoints of ABCD; LMNO is formed similarly from EFGH. A circle is inscribed in EFGH and has area 38.5 sq cm. Find the area (in sq cm) of square ABCD.

Introduction / Context:
Joining midpoints of a square creates a new square whose area is exactly half of the original. An inscribed circle in the inner square relates its area to the inner square’s area through the radius being half the side of that square.

Given Data / Assumptions:

• Area(circle inscribed in EFGH) = 38.5 cm^2.
• Area(EFGH) = (side_E)^2.
• For an inscribed circle, radius r = side_E/2, so area = πr^2 = (π/4)*side_E^2.
• Area(EFGH) = (1/2)*Area(ABCD).

Concept / Approach:
From circle area = (π/4) * area(EFGH), recover area(EFGH). Then double it to find area(ABCD). Use π = 22/7 as is standard for aptitude arithmetic with 38.5.

Step-by-Step Solution:

Verification / Alternative check:
Working backwards: area(EFGH) = 49; inscribed circle area = (π/4)*49 = 38.5 with π = 22/7, consistent.

Why Other Options Are Wrong:
196, 122.5, 171.5, 84 do not satisfy the (π/4) scaling and the 1/2 area relation between ABCD and EFGH.

Common Pitfalls:
Using diagonal/2 instead of side/2 for circle radius, or forgetting the 1/2 area relationship between the two squares.

Final Answer:
98