MathDB
Median perpendicular to line.

Source: Vietnam TST 2019 Day 2 P5

March 30, 2019
geometry

Problem Statement

Given a scalene triangle ABCABC inscribed in the circle (O)(O). Let (I)(I) be its incircle and BI,CIBI,CI cut AC,ABAC,AB at E,FE,F respectively. A circle passes through EE and touches OBOB at BB cuts (O)(O) again at MM. Similarly, a circle passes through FF and touches OCOC at CC cuts (O)(O) again at NN. ME,NFME,NF cut (O)(O) again at P,QP,Q. Let KK be the intersection of EFEF and BCBC and let PQPQ cuts BCBC and EFEF at G,HG,H, respectively. Show that the median correspond to GG of the triangle GHKGHK is perpendicular to IOIO.
Back to ProblemsView on AoPS