MathDB
Mixtilinear again

Source: 2020 China Southeast 10.2

August 9, 2020
geometrycircumcircleincenter

Problem Statement

In a scalene triangle ΔABC\Delta ABC, AB<ACAB<AC, PBPB and PCPC are tangents of the circumcircle (O)(O) of ΔABC\Delta ABC. A point RR lies on the arc AC^\widehat{AC}(not containing BB), PRPR intersects (O)(O) again at QQ. Suppose II is the incenter of ΔABC\Delta ABC, ID⊥BCID \perp BC at DD, QDQD intersects (O)(O) again at GG. A line passing through II and perpendicular to AIAI intersects AB,ACAB,AC at M,NM,N, respectively. Prove that, if AR∥BCAR \parallel BC, then A,G,M,NA,G,M,N are concyclic.
Back to ProblemsView on AoPS