Trirectangular Corner Locus

Geometry Level 5

Given a circle of radius 11, the locus of all PP such that there are points A,B,CA, B, C on the circle such that

APB=BPC=CPA=90°\angle APB=\angle BPC=\angle CPA=90°

is a surface of a solid that has a volume VV. Find 100V\left\lfloor 100V \right\rfloor

This is a 3D generalization of the fact that the locus of all PP on a circle makes a right triangle with the diameter.

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