MathDB

6

Part of 2006 German National Olympiad

Problems(1)

A Geometry problem

Source: German Mathematical Olympiad Final Round, Grades 12-13 YEAR-2006

1/15/2016
Let a circle through BB and CC of a triangle ABCABC intersect ABAB and ACAC in YY and ZZ , respectively. Let PP be the intersection of BZBZ and CYCY , and let XX be the intersection of APAP and BCBC . Let MM be the point that is distinct from XX and on the intersection of the circumcircle of the triangle XYZXYZ with BCBC. Prove that MM is the midpoint of BCBC
geometry