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The Talmud Sotah (32b) explains, that the reason the sin offering (Chatos) and the burnt offering (Olah) were slaughtered in the same place, by the northern part of the Mizbayach, was to save sinners from embarrassment. Anyone witnessing someone bringing a Chatos could assume that it was a Olah, which is brought as a donation and not necessarily as kaparah for an aveira.
Using this as a source, the Sages made a regulation that Shmoneh Esreh must be recited quietly, in order not to embarrass people who confess their aveiros during their tefilah.
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