Lost in space

Geometry Level 3

A point PP in R3\mathbb{R}^{3} has distances of 3,7,8,93,7,8,9 and 1111 from five of the vertices of a regular octahedron. If the distance from the sixth vertex of the octahedron to PP is a\sqrt{a}, where aa is a positive, square-free integer, then find aa .

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