A circle is inscribed in an equilateral triangle of side `adot` The area of any square inscribed in this circle is ______.

Explanation

To find the area of any square inscribed in a circle that is inscribed in an equilateral triangle of side length \( a \), we can follow these steps:

### Step 1: Find the radius of the inscribed circle (inradius)
For an equilateral triangle with side length \( a \), the formula for the inradius \( R \) is given by:

\[ R = \frac{a}{2\sqrt{3}} \]
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