MathDB

9.7

Part of 1993 All-Russian Olympiad Regional Round

Problems(1)

collinear wanted, AE = NE, CE = ME, rhombus related

Source: Oral Moscow Team MO 2017 IX p5 / All-Russian MO 1993 Regional (Round 4) 9.7

9/19/2020
On the diagonal ACAC of the rhombus ABCDABCD, a point EE is taken, which is different from points AA and CC, and on the lines ABAB and BCBC are points NN and MM, respectively, with AE=NEAE = NE and CE=MECE = ME. Let KK be the intersection point of lines AMAM and CNCN. Prove that points K,EK, E and DD are collinear.
geometryrhombuscollinearequal segments