# 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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