# 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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