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Boring Geometry: Easy Exercise of Method of Moving Point

Source: 2022 IRN TWN Friendly Math Competition P4

June 24, 2022
geometrymoving pointsTaiwanIran

Problem Statement

Given an acute triangle ABCABC, let PP be an arbitrary point on segment BCBC. A line passing through PP and perpendicular to ACAC intersects ABAB at PbP_b. A line passing through PP and perpendicular to ABAB intersects ACAC at PcP_c. Prove that the circumcircle of triangle APbPcAP_bP_c passes through a fixed point other than AA when PP varies on segment BCBC.
Proposed by ltf0501
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