MathDB
Reposted

Source: IMO Shortlist 2018 G4

July 17, 2019
IMO Shortlistgeometryconcurrency

Problem Statement

A point TT is chosen inside a triangle ABCABC. Let A1A_1, B1B_1, and C1C_1 be the reflections of TT in BCBC, CACA, and ABAB, respectively. Let Ω\Omega be the circumcircle of the triangle A1B1C1A_1B_1C_1. The lines A1TA_1T, B1TB_1T, and C1TC_1T meet Ω\Omega again at A2A_2, B2B_2, and C2C_2, respectively. Prove that the lines AA2AA_2, BB2BB_2, and CC2CC_2 are concurrent on Ω\Omega.
Proposed by Mongolia
Back to ProblemsView on AoPS