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Regional Olympiad - FBH 2017 Grade 12 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2017

September 19, 2018

geometryangle bisector

Problem Statement

In triangle

ABC

on side

AC

are points

K

L

and

M

such that

BK

is an angle bisector of

\angle ABL

BL

is an angle bisector of

\angle KBM

and

BM

is an angle bisector of

\angle LBC

, respectively. Prove that

4 \cdot LM <AC

and

3\cdot \angle BAC - \angle ACB < 180^{\circ}