This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 1

2021 Turkey MO (2nd round), 4
Tags: angle bisector , z -orthocenter , geometry
Points $D$ and $E$ are taken on $[BC]$ and $[AC]$ of acute angled triangle $ABC$ such that $BD$ and $CE$ are angle bisectors. Projections of $D$ onto $BC$ and $BA$ are $P$ and $Q$, projections of $E$ onto $CA$ and $CB$ are $R$ and $S$. Let $AP \cap CQ=X$, $AS \cap BR=Y$ and $BX \cap CY=Z$. Show that $AZ \perp BC$.