Trirectangular Corner Locus

Geometry Level 5

Given a circle of radius \(1\), the locus of all \(P\) such that there are points \(A, B, C\) on the circle such that

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

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

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


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