Perimeter / Radius = \( 2 \pi \)

Geometry Level 3

\(AB\) is a diameter of the circle above, and \(C\) is a point on the circumference such that
\[ \frac { \text{Area of Circle} } { \text{ Area of } \triangle ABC } = 2 \pi. \] If \( \angle B < \angle A \), what is the measure of \(\angle B\) in degrees?

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