MathDB

2

Part of 2005 Regional Competition For Advanced Students

Problems(1)

36th Austrian Mathematical Olympiad 2005

Source: round 1, problem 2

2/11/2009
Construct the semicircle h h with the diameter AB AB and the midpoint M M. Now construct the semicircle k k with the diameter MB MB on the same side as h h. Let X X and Y Y be points on k k, such that the arc BX BX is 32 \frac{3}{2} times the arc BY BY. The line MY MY intersects the line BX BX in D D and the semicircle h h in C C. Show that Y Y ist he midpoint of CD CD.
geometry unsolvedgeometry