MathDB

2

Part of 2017 Serbia National Math Olympiad

Problems(2)

Geometry, Serbia MO 2017

Source: Serbia MO 2017 P2

4/1/2017
Let ABCDABCD be a convex and cyclic quadrilateral. Let AD∩BC={E}AD\cap BC=\{E\}, and let M,NM,N be points on AD,BCAD,BC such that AM:MD=BN:NCAM:MD=BN:NC. Circle around △EMN\triangle EMN intersects circle around ABCDABCD at X,YX,Y prove that AB,CDAB,CD and XYXY are either parallel or concurrent.
geometrycyclic quadrilateral
Chess combinatorics

Source: Serbia National Mathematical Olympiad 2017, Day 2, Problem 2

4/2/2017
Find the maximum number of queens you could put on 2017×20172017 \times 2017 chess table such that each queen attacks at most 11 other queen.
combinatorics