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A_iA_j //A_kA_i then A_{i'}A_{j'} // A_{k'}A_{i'}

Source: 2004 Estonia National Olympiad Final Round grade 12 p5

March 25, 2020
polygonparallelperpendiculargeometrycombinatorial geometry

Problem Statement

Let nn and cc be coprime positive integers. For any integer ii, denote by i′i' the remainder of division of product cici by nn. Let Ao.A1,A2,...,An−1A_o.A_1,A_2,...,A_{n-1} be a regular nn-gon. Prove that a) if AiAj∥AkAiA_iA_j \parallel A_kA_i then Ai′Aj′∥Ak′Ai′A_{i'}A_{j'} \parallel A_{k'}A_{i'} b) if AiAj⊥AkAlA_iA_j \perp A_kA_l then Ai′Aj′⊥Ak′Al′A_{i'}A_{j'} \perp A_{k'}A_{l'}
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