I’ve posted for this feast before, but today here is a bit of geekishness.
The date of the Annunciation is fixed at 9 months before the date of Christmas (which is, in any case, an ‘official birthday’), by the simple process of keeping the 25 and working 9 months backwards (without allowing for different month lengths), because everybody knows that a pregnancy lasts about 9 months.
However, the average time for pregnancy reckoned from the date of last period (rather than conception, since dates of periods are easier to determine) is actually 40 weeks, which is approximately 9 months and one week. If you assume that Jesus was conceived at the Annunciation (at the time that Mary said yes), then that would (taken the normal times of things) be about 38 weeks. 38 weeks before Christmas day is approximately the 3rd April.