MathDB
Show that 2MN=BM+CN

Source: P2: Bosnia and Herzegovina TST 2002

September 30, 2014
geometrytrapezoidgeometry unsolved

Problem Statement

Triangle ABCABC is given in a plane. Draw the bisectors of all three of its angles. Then draw the line that connects the points where the bisectors of angles ABCABC and ACBACB meet the opposite sides of the triangle. Through the point of intersection of this line and the bisector of angle BACBAC, draw another line parallel to BCBC. Let this line intersect ABAB in MM and ACAC in NN. Prove that 2MN=BM+CN2MN = BM+CN.
Back to ProblemsView on AoPS