# Reuleaux's Revolution

Geometry Level 5

The Reuleaux triangle is constructed by drawing an equilateral triangle $$XYZ$$ and drawing the three circular arcs: $$YZ$$ with center $$X$$, $$XZ$$ with center $$Y$$, and $$XY$$ with center $$Z$$. When this figure is rotated about it's axis of symmetry it forms a solid of constant width the Reuleaux Triangle Spheroform.

Let $$A$$ be the apex point, $$B$$ be the bottom point, and $$C$$ be the centroid point, all of which are on the axis of revolution. Find $$\dfrac{AC}{ AB}$$.