Specimen Cyprus Seniors Provincial/2nd grade/Problem 1
Problem
Let $\Alpha\Beta\Gamma\Delta$ (Error compiling LaTeX. Unknown error_msg) be a parallelogram. Let 
be a straight line passing through $\Alpha$ (Error compiling LaTeX. Unknown error_msg) without cutting $\Alpha\Beta\Gamma\Delta$ (Error compiling LaTeX. Unknown error_msg). If $\Beta ', \Gamma ', \Delta '$ (Error compiling LaTeX. Unknown error_msg) are the projections of $\Beta, \Gamma, \Delta$ (Error compiling LaTeX. Unknown error_msg) on respectively, show that
a) the distance of 
from is equal to the sum of the distances $\Beta, \Delta$ (Error compiling LaTeX. Unknown error_msg) from .
b)Area$(\Beta\Gamma\Delta)$ (Error compiling LaTeX. Unknown error_msg)=Area$(\Beta '\Gamma '\Delta ')$ (Error compiling LaTeX. Unknown error_msg).
