# Specimen Cyprus Seniors Provincial/2nd grade/Problems

## 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: .