MathDB
JBMO Shortlist 2022 G6

Source: JBMO Shortlist 2022

June 26, 2023
geometrytangentcollinearJuniorBalkanshortlist

Problem Statement

Let ABCABC be a right triangle with hypotenuse BCBC. The tangent to the circumcircle of triangle ABCABC at AA intersects the line BCBC at TT. The points DD and EE are chosen so that AD=BD,AE=CE,AD = BD, AE = CE, and ∠CBD=∠BCE<90∘\angle CBD = \angle BCE < 90^{\circ}. Prove that D,E,D, E, and TT are collinear.
Proposed by Nikola Velov, Macedonia
Back to ProblemsView on AoPS