Geometric Serious?

Geometry Level pending

A circle \(C_0\) is inscribed in an equilateral triangle \(XYZ\) of side length \(112.\) Then, for each positive integer \(n,\) circle \(C_n\) is inscribed in the region bounded by \(XY , XZ,\) and an arc of circle \(C_{n−1},\) forming an infinite sequence of circles tangent to sides \(XY\) and \(XZ\) and approaching vertex \(X.\) If these circles collectively have area \(m\pi,\) find \(m. \)

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