# Cube in a cone

Geometry Level pending

A cone has a circular base of radius 120 centimeters and center $$O$$, and a vertex $$V$$ that is $$240\sqrt{2}$$ centimeters directly above $$O$$. A cube is placed such that it has 4 vertices on the circular base, and 4 vertices on the lateral side of the cone. The side length of the cube can be expressed as $$a \sqrt{b}$$, where $$a$$ and $$b$$ are positive integers, and $$b$$ is not divisible by the square of any prime. What is $$a+b$$?

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