C. 886. The wall of a building is decorated by a square with its circumscribed circle drawn. There is a semicircle drawn outwards on each side of the square as a diameter, so that the circular arcs form four crescent shaped figures. What is the length of the side of the square if the area of such a crescent is 1 m^{2}?
(5 points)
Deadline expired on 19 March 2007.
Google Translation (Sorry, the solution is published in Hungarian only.)
Megoldás. Jelölje a négyzet oldalát x. Ekkor egy Hold alakú mező területe:
=x^{2}(/8/8+1/4)=x^{2}/4.
Vagyis 1=x^{2}/4, ahonnan x=2 m.
Statistics on problem C. 886.  410 students sent a solution.  
5 points:  357 students. 
4 points:  8 students. 
3 points:  35 students. 
2 points:  7 students. 
0 point:  2 students. 
Unfair, not evaluated:  1 solution. 


Problems in Mathematics of KöMaL, February 2007
