MathDB

1

Part of 2017 Israel Oral Olympiad

Problems(1)

Area of a Dragon

Source: Israeli Oral Olympiad #1

1/18/2017
ABCDEFGABCDEFG is a convex polygon with area 1. Points X,Y,Z,U,VX,Y,Z,U,V are arbitrary points on AB,BC,CD,EF,FGAB, BC, CD, EF, FG. Let M,I,N,K,SM, I, N, K, S be the midpoints of EZ,BU,AV,FX,TEEZ, BU, AV, FX, TE. Find the largest and smallest possible values of the area of AKBSCMDEIFNGAKBSCMDEIFNG.
geometry