MathDB
CVM 2020 - RE - P3

Source: CVM 2020

July 16, 2020
geometry

Problem Statement

Consider (△n=AnBnCn)n≥1\left(\triangle_n=A_nB_nC_n\right)_{n\ge 1}. We define points An′,Bn′,Cn′A_n',B_n',C_n' in sides CnBn,AnCn,BnAnC_nB_n,A_nC_n,B_nA_n such that (n+1)BnAn′=CnAn′, (n+1)CnBn′=AnBn′, (n+1)AnCn′=BnCn′(n+1)B_nA_n'=C_nA_n',~(n+1)C_nB_n'=A_nB_n',~(n+1)A_nC_n'=B_nC_n'△n+1\triangle_{n+1} is defined by the intersections of AnAn′,BnBn′,CnCn′A_nA_n',B_nB_n',C_nC_n'. If SnS_n denotes the area of △n\triangle_n. Find S1S2020\frac{S_1}{S_{2020}}.
Proposed by Alejandro Madrid, Valle
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