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