A circular backyard swimming pool is 21 yards around the outside a bout how wide is the pool at its widest point?

About 20 feet.

In a circle, the widest point will be its diameter.

The distance round the circle is called its circumference (21 yards for your pool), and that is the diameter multiplied by pi. So the diameter is the circumference divided by pi. Pi is a never-ending number, but we'll use the short version of 3.142.

So the diameter of your pool is 21 yards divided by 3.142, or 63 feet / 3.142 = 20.05 ft.

I think we can safely ignore the 0.05 feet (just over half an inch).