MathDB
JBMO Shortlist 2021 G3

Source: JBMO Shortlist 2021

July 2, 2022
JuniorBalkanshortlist2021geometryconcurrency

Problem Statement

Let ABCABC be an acute triangle with circumcircle ω\omega and circumcenter OO. The perpendicular from AA to BCBC intersects BCBC and ω\omega at DD and EE, respectively. Let FF be a point on the segment AEAE, such that 2⋅FD=AE2 \cdot FD = AE. Let ll be the perpendicular to OFOF through FF. Prove that ll, the tangent to ω\omega at EE, and the line BCBC are concurrent.
Proposed by Stefan Lozanovski, Macedonia
Back to ProblemsView on AoPS