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 A_{1} and B_{1}, respectively. Similarly, let the line through Q, perpendicular to QR, meet CI and DI at C_{1} and D_{1}, respectively. Show that A_{1}D_{1}=B_{1}C_{1}.
Proposed by: Géza Bohner, Budapest
(5 pont)
Deadline expired on 15 January 2009.
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