2006 Seniors Pancyprian/2nd grade/Problem 4
Problem
A quadrilateral $\Alpha\Beta\Gamma\Delta$ (Error compiling LaTeX. Unknown error_msg), that has no parallel sides, is inscribed in a circle, its sides $\Delta\Alpha$ (Error compiling LaTeX. Unknown error_msg), $\Gamma\Beta$ (Error compiling LaTeX. Unknown error_msg) meet at $\Epsilon$ (Error compiling LaTeX. Unknown error_msg) and its sides $\Beta\Alpha$ (Error compiling LaTeX. Unknown error_msg), 
meet at $\Zeta$ (Error compiling LaTeX. Unknown error_msg).
If the bisectors of of $\angle\Delta\Epsilon\Gamma$ (Error compiling LaTeX. Unknown error_msg) and $\angle\Gamma\Zeta\Beta$ (Error compiling LaTeX. Unknown error_msg) intersect the sides of the quadrilateral at th points $\Kappa, \Lambda, \Mu, \Nu$ (Error compiling LaTeX. Unknown error_msg) prove that
i)the bisectors intersect normally
ii)the points $\Kappa, \Lambda, \Mu, \Nu$ (Error compiling LaTeX. Unknown error_msg) are vertices of a rhombus.
