MathDB

G3

Part of 2023-IMOC

Problems(1)

Configuration with cyclic quadrilateral

Source: IMOC 2023 G3

9/9/2023
ABCDABCD is a cyclic quadrilateral with circumcenter OO. The lines AC,BDAC, BD intersect at EE and AD,BCAD, BC intersect at FF. O1O_1 and O2O_2 are the circumcenters of △ABE\triangle ABE and △CDE\triangle CDE, respectively. Assume that (ABCD)(ABCD) and (OO1O2)(OO_1O_2) intersect at two points P,QP, Q. Prove that P,Q,FP, Q, F are collinear.
geometrycyclic quadrilateral