Q.Our birch tree has a 10 feet circumference measured 3 feet from ground level. How old is my tree?
We live in Toronto Ontario, Canada.

I would guess about 80 years old if it's a landscape tree. But according to the method reviewed in this article, it could be well over 100. If it's a white birch 36" in diameter, this method puts it at 180 yo. https://www.hunker.com/12001364/how-to-tell-the-age-of-a-tree-without-cutting-it-down
There are some big variables depending on the species of birch and the growing conditions. They don't all grow in girth at the same rate in different situations. Trees that are planted in landscapes that are irrigated and fertilized can grow much faster than trees in natural habitat. A birch on the bank of a pond or creek may out grow one in a drier environment.