Observable Planets

Geometry Level 2

A circle is inscribed in an equilateral triangle. A smaller circle is drawn such that it is tangent to two sides of the triangle as well as the larger circle.

The area of the equilateral triangle is \( a \sqrt{b} \), where \(a\) and \(b\) are positive integers with \(b\) square-free. Find \( a + b. \)

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