KöMaL - Középiskolai Matematikai és Fizikai Lapok
Sign In
Sign Up


Problem A. 529. (February 2011)

A. 529. There is given a circle k on the plane, a chord AB of k, furthermore four interior points, C, D, E and F, on the line segment AB. Draw an arbitrary chord X1X2 of k through point C, a chord Y1Y2 through D, a chord U1U2 through E, finally a chord V1V2 through F in such a way that X1, Y1, U1 and V1 lie on the same side of the line AB, and

\frac{AX_1\cdot BX_2}{X_1X_2} =\frac{AY_2\cdot BY_1}{Y_1Y_2} =\frac{AU_1\cdot
BU_2}{U_1U_2} =\frac{AV_2\cdot BV_1}{V_1V_2}

holds. Let Z be the intersection of the lines X1X2 and Y1Y2, and let W be the intersection of U1U2 and V1V2. Show that the lines ZW obtained in this way are concurrent or they are parallel to each other.

(5 pont)

Deadline expired on 10 March 2011.


3 students sent a solution.
5 points:Nagy 235 János, Nagy 648 Donát.
2 points:1 student.

Our web pages are supported by:   Ericsson   Cognex   Emberi Erőforrás Támogatáskezelő   Emberi Erőforrások Minisztériuma   Nemzeti Tehetség Program    
MTA Energiatudományi Kutatóközpont   MTA Wigner Fizikai Kutatóközpont     Nemzeti
Kulturális Alap   ELTE   Morgan Stanley