MathDB

Bosnia and Herzegovina TST 2000 Day 2 Problem 3

Source: Bosnia and Herzegovina Team Selection Test 2000

September 19, 2018

geometryparallelconcurrent

Problem Statement

It is given triangle

ABC

such that

\angle ABC = 3 \angle CAB

. On side

AC

there are two points

M

and

N

in order

A - N - M - C

and

\angle CBM = \angle MBN = \angle NBA

. Let

L

be an arbitrary point on side

BN

and

K

point on

BM

such that

LK \mid \mid AC

. Prove that lines

AL

NK

and

BC

are concurrent