Could it get any more regular?

Geometry Level 3

\(\Delta ABC\) is inscribed in a circle such that \(864 \angle A = \angle B = \angle C\). If \(B\) and \(C\) are adjacent vertices of a regular \(n\)-gon inscribed in the circle, find \(n\).

Details and Assumptions

  • The diagram above is (extremely) not to scale.
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