MathDB

G3

Part of 2022-IMOC

Problems(1)

A, O_P, O_Q, R are concylic

Source: 2022 IMOC G3 https://artofproblemsolving.com/community/c6h2918249p26069468

9/5/2022
Let △ABC\vartriangle ABC be an acute triangle. RR is a point on arc BCBC. Choose two points P,QP, Q on ARAR such that B,P,C,QB,P,C,Q are concyclic. Let the second intersection of BPBP, CPCP, BQBQ, CQCQ and the circumcircle of △ABC\vartriangle ABC is PBP_B, PCP_C, QBQ_B, QCQ_C, respectively. Let the circumcenter of △PPBPC\vartriangle P P_BP_C and △QQBQC\vartriangle QQ_BQ_C are OPO_P and OQO_Q, respectively. Prove that A,OP,OQ,RA,O_P,O_Q,R are concylic.
proposed by andychang
geometryConcyclic