MathDB
Parallel Lines of Circumcenters

Source: KMO 2022 P2

October 29, 2022
geometrycircumcircleCircumcenterparallel

Problem Statement

In a scalene triangle ABCABC, let the angle bisector of AA meets side BCBC at DD. Let E,FE, F be the circumcenter of the triangles ABDABD and ADCADC, respectively. Suppose that the circumcircles of the triangles BDEBDE and DCFDCF intersect at P(≠D)P(\neq D), and denote by O,X,YO, X, Y the circumcenters of the triangles ABC,BDE,DCFABC, BDE, DCF, respectively. Prove that OPOP and XYXY are parallel.
Back to ProblemsView on AoPS