An object is formed by removing a cylinder of radius $$\(\frac{2}{3} a\)$$ and height $$\(k h(k< 1)\)$$ from a uniform solid cylinder of radius $$\(a\)$$ and height $$\(h\)$$. The vertical axes of symmetry of the two cylinders coincide. The upper faces of the two cylinders are in the same plane as each other. The points $$\(A\)$$ and $$\(B\)$$ are the opposite ends of a diameter of the upper face of the object (see diagram). Given that $$\(h=\frac{8}{3} a\)$$, find the possible values of $$\(k\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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