Vietnam tst 2004
Posted: Wed May 23, 2012 1:25 am
It was number 5.
Let $A_{1},B_{1},C_{1},D_{1},E_{1}, F_{1}$ be the midpoints of the sides $AB, BC, CD, DE, EF, FA$ respectively of a hexagon $ABCDEF$. Let $p$ be the perimeter of hexagon $ABCDEF$ and $p_{1}$ be that of $A_{1}B_{1}C_{1}D_{1}E_{1} F_{1}$ .Suppose that the hexagon $A_{1}B_{1}C_{1}D_{1}E_{1}F_{1}$ has equal angles. Prove that $p ≥\frac {2}{\sqrt 3}p_{1}$. When does equality hold?.
My $100th$ post!!
Let $A_{1},B_{1},C_{1},D_{1},E_{1}, F_{1}$ be the midpoints of the sides $AB, BC, CD, DE, EF, FA$ respectively of a hexagon $ABCDEF$. Let $p$ be the perimeter of hexagon $ABCDEF$ and $p_{1}$ be that of $A_{1}B_{1}C_{1}D_{1}E_{1} F_{1}$ .Suppose that the hexagon $A_{1}B_{1}C_{1}D_{1}E_{1}F_{1}$ has equal angles. Prove that $p ≥\frac {2}{\sqrt 3}p_{1}$. When does equality hold?.
My $100th$ post!!