MathDB

3

Part of 2006 Costa Rica - Final Round

Problems(1)

Prove the existence of this triangle.

Source: Costarrican Math Olympiad 2006 - Problem 3.

5/20/2006
Let ABCABC be a triangle. Let P,Q,RP, Q, R be the midpoints of BC,CA,ABBC, CA, AB respectively. Let U,V,WU, V, W be the midpoints of QR,RP,PQQR, RP, PQ respectively. Let x=AU,y=BV,z=CWx=AU, y=BV, z=CW. Prove that there exist a triangle with sides x,y,zx, y, z.
vectorgeometryparallelogramgeometry unsolved