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MathNet 2022-part-01 — 197 problems (EN–VI) Question 131

Math Olympiad Vault · MathNet 2022-part-01 — 197 problems (EN–VI)

Question 131

Let $ABCDV$ be a regular-based right pyramid with apex at $V$. The plane $\lambda$ intersects the edges $VA$, $VB$, $VC$, and $VD$ at points $M$, $N$, $P$, and $Q$, respectively. Compute the ratio $VQ:QD = p:q$, if $VM:MA = 2:1$, $VN:NB = 1:1$, and $VP:PC = 1:2$.