Specimen Cyprus Seniors Provincial/2nd grade/Problem 1

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Problem

Let $AB\Gamma\Delta$ be a parallelogram. Let $(\epsilon)$ be a straight line passing through $A$ without cutting $AB\Gamma\Delta$. If $B', \Gamma ', \Delta '$ are the projections of $B, \Gamma, \Delta$ on $(\epsilon)$ respectively, show that

a) the distance of $\Gamma$ from $(\epsilon)$ is equal to the sum of the distances $B, \Delta$ from $(\epsilon)$.

b)Area($B\Gamma\Delta$)=Area($B'\Gamma '\Delta '$)

Solution


See also