Geometric Serious?

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 $m.$