MathDB

2006.9.4

Part of Kyiv City MO Juniors 2003+ geometry

Problems(1)

concurrency in a parallelogram (Kyiv City Olympiad 2006 9.4)

Source:

6/28/2020
On the sides ABAB and CDCD of the parallelogram ABCDABCD mark points EE and FF, respectively. On the diagonals ACAC and BDBD chose the points MM and NN so that EM∥BDEM\parallel BD and FN∥ACFN\parallel AC. Prove that the lines AF,DEAF, DE and MNMN intersect at one point.
(B. Rublev)
geometryparallelogramconcurrencyconcurrent