Specimen Cyprus Seniors Provincial/2nd grade/Problem 1

Problem

Let $\Alpha\Beta\Gamma\Delta$ (Error compiling LaTeX. Unknown error_msg) be a parallelogram. Let $(\epsilon)$ 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 $(\epsilon)$ respectively, show that

a) the distance of $\Gamma$ from $(\epsilon)$ is equal to the sum of the distances $\Beta, \Delta$ (Error compiling LaTeX. Unknown error_msg) from $(\epsilon)$.

b)Area$(\Beta\Gamma\Delta)$ (Error compiling LaTeX. Unknown error_msg)=Area$(\Beta '\Gamma '\Delta ')$ (Error compiling LaTeX. Unknown error_msg).

Solution


See also