MathDB
Plane through the edges of pyramid must be parallel to base

Source: Romanian TST 1997

September 17, 2011
geometry3D geometrypyramidgeometry proposed

Problem Statement

Let VA1A2…AnVA_1A_2\ldots A_n be a pyramid, where n≥4n\ge 4. A plane Π\Pi intersects the edges VA1,VA2,…,VAnVA_1,VA_2,\ldots, VA_n at the points B1,B2,…,BnB_1,B_2,\ldots,B_n respectively such that the polygons A1A2…AnA_1A_2\ldots A_n and B1B2…BnB_1B_2\ldots B_n are similar. Prove that the plane Π\Pi is parallel to the plane containing the base A1A2…AnA_1A_2\ldots A_n.
Laurentiu Panaitopol
Back to ProblemsView on AoPS