This is an announcement for the paper "Products of orthogonal projections and polar decompositions" by Gustavo Corach and Alejandra Maestripieri. Abstract: We characterize the sets $\XX$ of all products $PQ$, and $\YY$ of all products $PQP$, where $P,Q$ run over all orthogonal projections and we solve the problems \newline $\arg\min\{\|P-Q\|: (P,Q) \in \cal Z\}$, for $\cal Z=\XX$ or $\YY.$ We also determine the polar decompositions and Moore-Penrose pseudoinverses of elements of $\XX.$ Archive classification: math.FA Mathematics Subject Classification: 47A05 Submitted from: gcorach@fi.uba.ar The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1011.5237 or http://arXiv.org/abs/1011.5237