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Ratios in a regular quadrangular pyramid

Source: 2022 Bulgarian Spring Math Competition, Problem 12.2

March 27, 2022
ratiopyramidgeometry3D geometry

Problem Statement

Let ABCDVABCDV be a regular quadrangular pyramid with VV as the apex. The plane λ\lambda intersects the VAVA, VBVB, VCVC and VDVD at MM, NN, PP, QQ respectively. Find VQ:QDVQ : QD, if VM:MA=2:1VM : MA = 2 : 1, VN:NB=1:1VN : NB = 1 : 1 and VP:PC=1:2VP : PC = 1 : 2.
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