Problem A. 515. (October 2010)

A. 515. There is given a triangle ABC. For every 0<t<1 let U(t) and V(t) be the points which divide the line segments AB and BC in the ratio t:(1-t), respectively. Prove that there is a parabola which is tangent to all lines U(t)V(t).

(5 pont)

Deadline expired on November 10, 2010.

Statistics:

13 students sent a solution.
5 points:	Ágoston Tamás, Backhausz Tibor, Bágyoni-Szabó Attila, Damásdi Gábor, Frankl Nóra, Kalina Kende, Mester Márton, Nagy 235 János, Nagy 648 Donát, Strenner Péter.
4 points:	Lenger Dániel, Weisz Ágoston.
3 points:	1 student.

Problems in Mathematics of KöMaL, October 2010