Three circles are drawn within triangle \(ABC\) such that no two circles overlap and that each is tangent to one another

[M7MBA]

Three circles are drawn within triangle \(ABC\) such that no two circles overlap and that each is tangent to one another and to the triangle in at least one place. What is their combined area?

(1) The radius of one of the circles is \(4.\)

(2) Triangle \(ABC\) is equilateral.

Answer: E

Source: Veritas Prep