MathDB
Easy Geo Regarding Euler Line

Source: 2021 Taiwan TST Round 2 Independent Study 1-G

April 7, 2021
EulergeometrycircumcircleTaiwan

Problem Statement

Let ABCDABCD be a convex quadrilateral with pairwise distinct side lengths such that AC⊥BDAC\perp BD. Let O1,O2O_1,O_2 be the circumcenters of ΔABD,ΔCBD\Delta ABD, \Delta CBD, respectively. Show that AO2,CO1AO_2, CO_1, the Euler line of ΔABC\Delta ABC and the Euler line of ΔADC\Delta ADC are concurrent.
(Remark: The Euler line of a triangle is the line on which its circumcenter, centroid, and orthocenter lie.)
Proposed by usjl
Back to ProblemsView on AoPS