MathDB

3

Part of 2022 Indonesia MO

Problems(1)

Rectangle geometry with concurrency

Source: Indonesia National Math Olympiad 2022 Problem 3 (INAMO 2022/3)

10/4/2022
Let ABCDABCD be a rectangle. Points EE and FF are on diagonal ACAC such that FF lies between AA and EE; and EE lies between CC and FF. The circumcircle of triangle BEFBEF intersects ABAB and BCBC at GG and HH respectively, and the circumcircle of triangle DEFDEF intersects ADAD and CDCD at II and JJ respectively. Prove that the lines GJ,IHGJ, IH and ACAC concur at a point.
geometryrectanglecircumcircleIndonesiaIndonesia MO