The side length of equilateral △ ABC is a, and the area of inscribed square defg of its inscribed circle is obtained

The side length of equilateral △ ABC is a, and the area of inscribed square defg of its inscribed circle is obtained

If the side length of equilateral △ ABC is a, ∵ point O is the inner part of △ ABC, ∵ OE ⊥ AB, AE = be = A2, ∠ EAO = 30 °, ∵ OE = AE · Tan ∠ EAO = 36a, then the side length of the square is 2oe · cos45 ° = 2 × 22oe = 2 × 22 × 36a = 66A. Then the area of the square is 16a2