Difference between revisions of "Specimen Cyprus Seniors Provincial/2nd grade/Problem 1"
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== Problem == | == Problem == | ||
| − | Let <math> | + | Let <math>\Alpha\Beta\Gamma\Delta</math> be a parallelogram. Let <math>(\epsilon)</math> be a straight line passing through <math>\Alpha</math> without cutting <math>\Alpha\Beta\Gamma\Delta</math>. If <math>\Beta ', \Gamma ', \Delta ' </math> are the projections of <math>\Beta, \Gamma, \Delta</math> on <math>(\epsilon)</math> respectively, show that |
| − | a) the distance of <math>\Gamma</math> from <math>(\epsilon)</math> is equal to the sum of the distances <math> | + | a) the distance of <math>\Gamma</math> from <math>(\epsilon)</math> is equal to the sum of the distances <math>\Beta, \Delta</math> from <math>(\epsilon)</math>. |
| − | b)Area | + | b)Area<math>(\Beta\Gamma\Delta)</math>=Area<math>(\Beta '\Gamma '\Delta ')</math>. |
== Solution == | == Solution == | ||
Latest revision as of 06:52, 12 November 2006
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).
