Problem A. 467. (December 2008)

A. 467. Let ABCD be a circumscribed trapezoid such that the lines AD and BC intersect at point R. Denote by I the incenter of the trapezoid, and let the incircle touch the sides AB and CD at points P and Q, respectively. Let the line through P, which is perpendicular to PR, meet the lines angle bisector AI and BI at points A₁ and B₁, respectively. Similarly, let the line through Q, perpendicular to QR, meet CI and DI at C₁ and D₁, respectively. Show that A₁D₁=B₁C₁.

Proposed by: Géza Bohner, Budapest

(5 pont)

Deadline expired on January 15, 2009.

Statistics:

6 students sent a solution.
5 points:	Éles András, Nagy 235 János, Nagy 314 Dániel, Nagy 648 Donát, Wolosz János.
4 points:	Tomon István.

Problems in Mathematics of KöMaL, December 2008