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Considering the planes of the frustum ABCDEF

Source: Romanian MO 2002

December 8, 2010
geometry3D geometryfrustumgeometry proposed

Problem Statement

Let [ABCDEF][ABCDEF] be a frustum of a regular pyramid. Let GG and G′G' be the centroids of bases ABCABC and DEFDEF respectively. It is known that AB=36,DE=12AB=36,DE=12 and GG′=35GG'=35. a)a) Prove that the planes (ABF),(BCD),(CAE)(ABF),(BCD),(CAE) have a common point PP, and the planes (DEC),(EFA),(FDB)(DEC),(EFA),(FDB) have a common point P′P', both situated on GG′GG'. b)b) Find the length of the segment [PP′][PP'].
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