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Pyramid and convex pentagon

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November 11, 2005
geometry3D geometrypyramidgeometry unsolved

Problem Statement

PABCDEPABCDE is a pyramid with ABCDEABCDE a convex pentagon. A plane meets the edges PA,PB,PC,PD,PEPA, PB, PC, PD, PE in points A′,B′,C′,D′,E′A', B', C', D', E' distinct from A,B,C,D,EA, B, C, D, E and PP. For each of the quadrilaterals ABB′A′,BCC′B,CDD′C′,DEE′D′,EAA′E′ABB'A', BCC'B, CDD'C', DEE'D', EAA'E' take the intersection of the diagonals. Show that the five intersections are coplanar.
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