Steve and his Pickaxe

Geometry Level pending

Steve has a pickaxe. The pickaxe's blade is an arc with a center that is \(30\) cm down the handle of the pickaxe. (Picture the pickaxe blade side up.) The arc's corresponding chord is bisected by the handle, making the handle an extension of the diameter of the circle of which the arc is a section. The arc's measure is \(\frac{\pi}{3}\) radians. What is the angle between the handle end of the pickaxe, the center of the arc, and either point of Steve's pickaxe? Give it in radians, rounded to the nearest hundredth of a radian. (Hint: the pickaxe is symmetric across the line which is an extension of its handle.)

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