3-D Geometry

Geometry Level 4

A point $$P$$ inside a regular tetrahedron is such that its distance from all vertices $$A, B, C$$ & $$D$$ of the tetrahedron is the same. The line $$AP$$, when produced, intersects the plane formed by vertices $$B, C$$ & $$D$$ at the point $$Q$$. The ratio $$\frac{AP}{AQ}$$ can be written as $$\frac{a}{b}$$.

Find $$a^{b}$$.

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