An alternative method, not using Heron's formula, is based on finding x in terms of a and b using the tangents of the angles at the centre of the circle. This problem was solved by Brad Rodgers, age 14 of Kokomo School, India and Sue Liu of Madras College, St Andrews. The volume of the whole cube is 64 cubic units so the ratio of the volume of the smaller piece to the volume of the cube is 7 to 48. The ratio of the volumes of the two pieces of the cube is 7 to 41. This has gone unsolved for a while.
Some points never touch, other points touch only once, other points touch twice.
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