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IMC 2009 Day 2 P1

Source:

July 15, 2014
IMCcollege contests

Problem Statement

Let ℓ\ell be a line and PP be a point in R3\mathbb{R}^3. Let SS be the set of points XX such that the distance from XX to ℓ\ell is greater than or equal to two times the distance from XX to PP. If the distance from PP to ℓ\ell is d>0d>0, find Volume(S)\text{Volume}(S).
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