0
$\begingroup$

In the city of Dakar, live three sisters, Eve, Marie and Anna. At night they play. That night, Eve is above the town hall, with her piercing eyes, she sees Marie 4 mile to the east and Anna 2 mile to the north. The rule of their game is simple, each one moves in turn on a line parallel to that which joins the other two but it can move the distance it wishes!

Can they (after several movements if necessary) meet: Eve at the Town Hall, Marie at 3 mile in the North-East and Anna at 3 mile in the South-East ?

$\endgroup$
2
  • $\begingroup$ What did you try? Where did you get stuck? What approaches didn't work? $\endgroup$
    – dimpol
    Commented Nov 25, 2016 at 16:01
  • $\begingroup$ I do not have a track. We are currently studying complex numbers. And I do not see any connection with this exercise and the chapter we are currently doing. $\endgroup$
    – yoda
    Commented Nov 25, 2016 at 16:15

1 Answer 1

Reset to default
3
$\begingroup$

No, the area of the triangle they form is constant, as the sister that moves will neither change the base (the line formed by the two nonmoving sisters) nor the height (her distance from the line, by definition, is constant). If any two sisters met, the area of the triangle would be zero, which cannot happen.

$\endgroup$
3
  • $\begingroup$ Since everyone can move from the distance she wishes how the area of the triangle could be constant ? $\endgroup$
    – yoda
    Commented Nov 25, 2016 at 16:11
  • $\begingroup$ Does the base of the triangle (two nonmoving sisters) change? What is the definition of "parallel"? $\endgroup$
    – AlgorithmsX
    Commented Nov 25, 2016 at 16:20
  • $\begingroup$ I see. You are right. Thank you. $\endgroup$
    – yoda
    Commented Nov 25, 2016 at 16:23

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .