MathDB

G5

Part of 2023-IMOC

Problems(1)

Special hexagon

Source: IMOC 2023 G5

9/9/2023
ABCDEFABCDEF is a cyclic hexagon with circumcenter OO, and AD,BE,CFAD, BE, CF are concurrent at XX. PP is a point on the plane. The circumenter of PABPAB is OABO_{AB}. Define OBC,OCDO_{BC}, O_{CD}, ODE,OEF,OFAO_{DE}, O_{EF}, O_{FA} similarly. Prove that OABODE,OBCOEF,OCDOFAO_{AB} O_{DE}, O_{BC}O_{EF}, O_{CD}O_{FA}, OXOX are concurrent.
geometry