Problem B. 3872. (January 2006)
B. 3872. The angle A of a triangle ABC is obtuse. Let D denote an arbitrary point on side AB, and let E be an arbitrary point on side AC. Show that CD+BE>BD+DE+EC.
(3 pont)
Deadline expired on February 15, 2006.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás: Tompaszögű háromszögben a tompaszöggel szemben van a leghosszabb oldal, így CD>CA és BE>BA. Az ADE háromszögben pedig DE<AD+AE. Ezért
CD+BE>BA+CA=BD+AD+AE+EC>BD+DE+EC.
Statistics:
197 students sent a solution. 3 points: 173 students. 2 points: 7 students. 1 point: 13 students. 0 point: 4 students.
Problems in Mathematics of KöMaL, January 2006