Mathematical and Physical Journal
for High Schools
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Problem B. 4752. (December 2015)

B. 4752. Consider circles \(\displaystyle k_1\) with center \(\displaystyle O_1\) and radius \(\displaystyle r_1\), and \(\displaystyle k_2\) with center \(\displaystyle O_2\) and radius \(\displaystyle r_2\). Line \(\displaystyle PA\) is tangent to \(\displaystyle k_1\) at \(\displaystyle A\) and line \(\displaystyle PD\) is tangent to \(\displaystyle k_2\) at \(\displaystyle D\). Segment \(\displaystyle AD\) intersects \(\displaystyle k_1\) and \(\displaystyle k_2\) at \(\displaystyle B\) and \(\displaystyle C\), respectively. Find \(\displaystyle PA/PD\) in terms of \(\displaystyle r_1\) and \(\displaystyle r_2\) if \(\displaystyle AB=CD\).

M&IQ

(4 pont)

Deadline expired on January 11, 2016.


Statistics:

127 students sent a solution.
4 points:Barabás Ábel, Baran Zsuzsanna, Bodolai Előd, Bukva Balázs, Busa 423 Máté, Csertán András, Csitári Nóra, Czirkos Angéla, Döbröntei Dávid Bence, Fuisz Gábor, Fülöp Anna Tácia, Glasznova Maja, Hornák Bence, Juhász 326 Dániel, Kasó Ferenc, Keresztfalvi Bálint, Kuchár Zsolt, Lakatos Ádám, Matolcsi Dávid, Mészáros Anna, Mikulás Zsófia, Nagy Dávid Paszkál, Németh 123 Balázs, Paulovics Péter, Polgár Márton, Schrettner Bálint, Schrettner Jakab, Szabó 417 Dávid, Szemerédi Levente, Tiszay Ádám, Tóth 111 Máté , Váli Benedek, Varsányi András, Viharos Loránd Ottó, Záhorský Ákos.
3 points:83 students.
2 points:2 students.
1 point:5 students.
Unfair, not evaluated:2 solutions.

Problems in Mathematics of KöMaL, December 2015