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
Deadline expired on 15 January 2009.