In a yard there is thrusted a 2 m heigh pole; at three o' clock sharp, from its top four flies take off in different directions; each one flies in a straight line and with a constant speed: the first one flies with 50m/min , the second one with 60m/min, the third one flies with 70m/min and the last one with 80m/min. 9 minutes later the four flies are situated in the same plane. When won't they be situated in the same plan any more?

Solution:
According to Thales theorem, they will be all the time situated in the same plane because flying in four different directions they will over at any moment a distance proportional to the distance covered by the other three flies.
Thales' theorem is: If we have two unparallel lines situated in the same plane and a secant, by drawing parallel lines to the given secanta we obtain proportional segment on the unparallel lines.

Petric Mihai and Sava Adrian, 9 grade A
Teacher: Ligia Garlea
"Alexandru Papiu Ilarian" Highschool Dej, Romania