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Regional Olympiad - FBH 2011 Grade 11 Problem 3

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2011

September 27, 2018
geometryangle bisector

Problem Statement

Let ADAD and BEBE be angle bisectors in triangle ABCABC. Let xx, yy and zz be distances from point MM, which lies on segment DEDE, from sides BCBC, CACA and ABAB, respectively. Prove that z=x+yz=x+y
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