First Problem, IMAR Competition 2012
-
Laurențiu Ploscaru
- Mesaje: 1237
- Membru din: Mie Mai 04, 2011 5:42 pm
- Localitate: Călimănești
- Contact:
First Problem, IMAR Competition 2012
Let $K$ be a convex planar set, symmetric about a point $O$, and let $X, Y, Z$ be three points in $K$. Show that $K$ contains the head of one of the vectors $\overrightarrow{OX}\pm \overrightarrow{OY},\ \overrightarrow{OY}\pm \overrightarrow{OZ},\ \overrightarrow{OZ}\pm \overrightarrow{OX}$.
People are strange when you're a stranger,
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.
Faces look ugly when you're alone.
Women seem wicked when you're unwanted,
Streets are uneven when you're down.