TR-MO-R1 2009 Problem 29

$ABCD$ kirişler dörtgeninin $[AC]$ ve $[BD]$ köşegenleri, $P$ noktasında kesişiyor. $APB$ ve $CPD$ üçgenlerinin çevrel çemberlerinin merkezleri, $ABCD$ dörtgeninin çevrel çemberi üstünde ve $|AC| + |BD| = 18$ ise, $ABCD$ dörtgeninin alanı nedir?

a) $36$ b) $\dfrac{81}{2}$ c) $\dfrac{36\sqrt{3}}{2}$ d) $\dfrac{81\sqrt{3}}{4}$ e) Hiçbiri

Official text Turkish Mathematical Olympiad, first round 2009 official paper, page 9. Quoted with source.

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