MathDB
OI _|_ BD iff AB + BC = 2AC

Source: 2021 2nd OMpD L3 P2 - Brazil - Olimpíada Matemáticos por Diversão

September 23, 2022
geometryperpendiculararc midpoint

Problem Statement

Let ABCABC be a triangle, Γ\Gamma its circumcircle and DD the midpoint of the arc ACAC of Γ\Gamma that does not contain BB. If OO is the center of Γ\Gamma and I is the incenter of ABCABC, prove that OIOI is perpendicular to BDBD if and only if AB+BC=2ACAB + BC = 2AC.
Back to ProblemsView on AoPS