# Difference between revisions of "Specimen Cyprus Seniors Provincial/2nd grade/Problems"

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Let <math>\text{A}\text{B}\Gamma\Delta</math> be a parallelogram. Let <math>(\epsilon)</math> be a straight line passing through <math>\text{A}</math> without cutting <math>\text{A}\text{B}\Gamma\Delta</math>. If <math>\text{B} ', \Gamma ', \Delta ' </math> are the projections of <math>\text{B}, \Gamma, \Delta</math> on <math>(\epsilon)</math> respectively, show that | Let <math>\text{A}\text{B}\Gamma\Delta</math> be a parallelogram. Let <math>(\epsilon)</math> be a straight line passing through <math>\text{A}</math> without cutting <math>\text{A}\text{B}\Gamma\Delta</math>. If <math>\text{B} ', \Gamma ', \Delta ' </math> are the projections of <math>\text{B}, \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>\text{B}</math> , <math>\Delta</math> from <math>(\epsilon)</math>. |

b) <math>\text{Area}(\text{B}\Gamma\Delta)=\text{Area}(\text{B} '\Gamma '\Delta ')</math>. | b) <math>\text{Area}(\text{B}\Gamma\Delta)=\text{Area}(\text{B} '\Gamma '\Delta ')</math>. |

## Latest revision as of 19:19, 18 January 2021

## Problem 1

Let be a parallelogram. Let be a straight line passing through without cutting . If are the projections of on respectively, show that

a) the distance of from is equal to the sum of the distances , from .

b) .

## Problem 2

If ,, and prove that

## Problem 3

Prove that if are positive integers, then the equation has irrational roots.

## Problem 4

If are the roots of equation then:

a) Prove that and

b) Calculate the value of: .