2006 Seniors Pancyprian/2nd grade/Problem 1
Problem
Let $\Alpha\Beta\Gamma$ (Error compiling LaTeX. Unknown error_msg) be a given triangle and $\Mu$ (Error compiling LaTeX. Unknown error_msg) the midpoint of the side $\Beta\Gamma$ (Error compiling LaTeX. Unknown error_msg). The circle with diameter $\Alpha\Beta$ (Error compiling LaTeX. Unknown error_msg) cuts $\Alpha\Gamma$ (Error compiling LaTeX. Unknown error_msg) at 
and form we bring $\Delta\Zeta=//\Mu\Gamma$ (Error compiling LaTeX. Unknown error_msg) ( is out of the triangle). Prove that the area of the quadrilateral $\Alpha\Mu\Gamma\Zeta$ (Error compiling LaTeX. Unknown error_msg) is equal to the area of the triangle $\Alpha\Beta\Gamma$ (Error compiling LaTeX. Unknown error_msg).
