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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