Library / /119 of 151

, 2022

Geometry Difficulty 8.0 Shortlist Prove it Hungary

Triangle $ABC$ has incenter $I$ and excircles $\Omega_A$ , $\Omega_B$ , and $\Omega_C$ . Let $\ell_A$ be the line through the feet of the tangents from $I$ to $\Omega_A$ , and define lines $\ell_B$ and $\ell_C$ similarly. Prove that the orthocenter of the triangle formed by lines $\ell_A$ , $\ell_B$ , and $\ell_C$ coincides with the Nagel point of triangle $ABC$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: KöMaL, licensed Rights held by KöMaL and the MATFUND Foundation. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.