At the side $AD=a$ of the square $ABCD$, we take the point $E$ and at the extension of $AB$ the point $Z$, such that $DE=BZ=x$. a) Show that the line bisector of $EZ$ goes through the vertex $C$. ...
This is a kind of a puzzle: I have a convex hull filled with $N$ small spheres(with radius $r$). Now, the balls grow in size till it hit any side of the Cavity (Convex hull) or any other ball. ...
P.S:I am looking for a hint and not the whole solution. BdMO 2012 nationals secondary: The vertices of a right triangle $ABC$ inscribed in a circle divide the circumference into three arcs. The ...