MathDB
Just messy figure geometry

Source: ISL 2018 G7

July 17, 2019
IMO Shortlistgeometry

Problem Statement

Let OO be the circumcentre, and Ω\Omega be the circumcircle of an acute-angled triangle ABCABC. Let PP be an arbitrary point on Ω\Omega, distinct from AA, BB, CC, and their antipodes in Ω\Omega. Denote the circumcentres of the triangles AOPAOP, BOPBOP, and COPCOP by OAO_A, OBO_B, and OCO_C, respectively. The lines ℓA\ell_A, ℓB\ell_B, ℓC\ell_C perpendicular to BCBC, CACA, and ABAB pass through OAO_A, OBO_B, and OCO_C, respectively. Prove that the circumcircle of triangle formed by ℓA\ell_A, ℓB\ell_B, and ℓC\ell_C is tangent to the line OPOP.
Back to ProblemsView on AoPS