In a circular table cover of radius 32 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in Figure. Find the area of the design.

Radius of circle = 32
Centroid O divides median AD into 2:1, therefore A0:0D = 2:1
= AO/OD = 2/1 ⇒ 32/OD = 2/1 ⇒ OD = 16
Therefore, AD = 32 + 16 = 48 cm
In AABD,
AB² = AD² + BD² = (48)² + (AB/2)²
⇒ 3/4 AB² = (48)² ⇒ AB = (48 × 2)/√3 = (96√3)/3 = 32√3
Area of equilateral triangle ABC
= √3/4 (32√3)² = 768√3 cm²
Area of circle
= πr² = π(32)² = 22/7 × 32 × 32 = 22528/7 cm²
Area of design = Area of circle – Area of equilateral triangle ABC
= (22528/7 – 768√3) cm²