3

Part of 2008 Bosnia and Herzegovina Junior BMO TST

Problems(1)

Nice geometry - paralellogram

Source: JBHMO (JBMO TST Bosnia and Herzegovina, Problem 3)

M

is given in the interior of parallelogram

ABCD

, and the point

N

inside triangle

AMD

is chosen so that < MNA \plus{} < MCB \equal{} MND \plus{} < MBC \equal{} 180^0. Prove that

MN

AB

geometryparallelogramtrapezoid