A Part of Circle

Geometry Level 5

A quadrant \(A_0 A_{90}\) of a unit circle is divided into 90 equal parts by inserting the points \(A_1,A_2, \ldots, A_{90}\) on the arc of the circle .

Let \(\displaystyle k = \sum_{i=1}^{90} Ar(\Delta A_0 O A_i) \).

Report your answer as \( \lfloor k \rfloor \).

\[\] Notation: \( \lfloor \cdot \rfloor \) denotes the floor function.


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