Problem A. 416. (January 2007)

A. 416. In a right triangle ABC, point F is the perpendicular foot of C on hypotenuse AB. Let point Q on AB be the perpendicular foot of a certain point P on leg AC. The line through B which is perpendicular to BP intersects line CF at point R. Show that the intersection of circles with diameters AC and FQ, different from F, lies in the interior of segment PR.

(5 pont)

Deadline expired on February 15, 2007.

Statistics:

12 students sent a solution.
5 points:	Bogár 560 Péter, Gyenizse Gergő, Hujter Bálint, Kisfaludi-Bak Sándor, Kónya 495 Gábor, Korándi Dániel, Lovász László Miklós, Nagy 224 Csaba, Nagy 235 János, Nagy 314 Dániel, Tomon István.
4 points:	Fischer Richárd.

Problems in Mathematics of KöMaL, January 2007