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Distances from a point inside a Tetrahedron

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April 6, 2013
geometry3D geometrytetrahedronprism

Problem Statement

Let ABCDABCD be a regular tetrahedron and let EE be a point inside the face ABCABC. Denote by ss the sum of the distances from EE to the faces DABDAB, DBCDBC, DCADCA, and by SS the sum of the distances from EE to the edges ABAB, BCBC, CACA. Then sS\dfrac sS equals
<spanclass=′latex−bold′>(A)</span>2<spanclass=′latex−bold′>(B)</span>223<spanclass=′latex−bold′>(C)</span>62<spanclass=′latex−bold′>(D)</span>2<spanclass=′latex−bold′>(E)</span>3<span class='latex-bold'>(A) </span>\sqrt2\qquad<span class='latex-bold'>(B) </span>\dfrac{2\sqrt2}3\qquad<span class='latex-bold'>(C) </span>\dfrac{\sqrt6}2\qquad<span class='latex-bold'>(D) </span>2\qquad<span class='latex-bold'>(E) </span>3
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