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PQ bisects AC if <BCD=90^o, A, B,C,D concyclic

Source: Mathematics Regional Olympiad of Mexico Northeast 2020 P2

September 7, 2022
bisects segmentgeometry

Problem Statement

Let AA, BB, CC and DD be points on the same circumference with ∠BCD=90∘\angle BCD=90^\circ. Let PP and QQ be the projections of AA onto BDBD and CDCD, respectively. Prove that PQPQ cuts the segment ACAC into equal parts.
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