# 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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