MathDB
2016 Japan Mathematical Olympiad Finals, Problem 2

Source:

February 17, 2016
geometry

Problem Statement

Let ABCDABCD be a concyclic quadrilateral such that AB:AD=CD:CB.AB:AD=CD:CB. The line ADAD intersects the line BCBC at XX, and the line ABAB intersects the line CDCD at YY. Let E, F, GE,\ F,\ G and HH are the midpoints of the edges AB, BC, CDAB,\ BC,\ CD and DADA respectively. The bisector of angle AXBAXB intersects the segment EGEG at SS, and that of angle AYDAYD intersects the segment FHFH at TT. Prove that the lines STST and BDBD are pararell.
Back to ProblemsView on AoPS