Correct : a

Given:
• A unit square has sides of length 1.
• Let the vertices of the unit square be (0,0), (1,0), (1,1), and (0,1).
• The midpoints of its sides are:
    • (0 + 1)/2, (0 + 0)/2 → (1/2, 0)
    • (1 + 1)/2, (0 + 1)/2 → (1, 1/2)
    • (1 + 0)/2, (1 + 1)/2 → (1/2, 1)
    • (0 + 0)/2, (1 + 0)/2 → (0, 1/2)
Determine the Rhombus Properties:
• The rhombus is formed by connecting these four midpoints. Let's denote the vertices as A=(1/2, 0), B=(1, 1/2), C=(1/2, 1), D=(0, 1/2).
• Side length (s): We can calculate the distance between any two adjacent midpoints, for example, A and B.
    s = √[(1 - 1/2)² + (1/2 - 0)²]
    s = √[(1/2)² + (1/2)²]
    s = √[1/4 + 1/4] = √[2/4] = √[1/2]
    s = 1/√2
• Diagonal lengths:
    • d₁ (distance between A and C) = √[(1/2 - 1/2)² + (1 - 0)²] = √[0² + 1²] = 1
    • d₂ (distance between B and D) = √[(1 - 0)² + (1/2 - 1/2)²] = √[1² + 0²] = 1
Calculate the Area of the Rhombus:
• The area of a rhombus can be calculated using its diagonals:
    Area = (d₁ × d₂) / 2
    Area = (1 × 1) / 2 = 1/2
Determine the Diameter of the Inscribed Circle:
• The diameter of the largest circle that can be inscribed within a rhombus is equal to the altitude (or height) of the rhombus.
• The area of a rhombus can also be calculated as: Area = side × altitude (h).
• Therefore, h = Area / side.
• Substitute the calculated values:
    h = (1/2) / (1/√2)
    h = (1/2) × √2
    h = √2 / 2
    h = 1/√2
• The diameter of the inscribed circle is equal to h.
• Diameter = 1/√2.