Div HEIGHT same as width to make a circle

I have an horizontal rectangle div container (parent)

with another smaller one inside (child).

I want to make the smaller one (child) look like a circle and the height should always be the same as the parent div for all resolutions.

I found a lot of solutions showing how to make a 1:1 proportional div (for instance, this example!) but all of them were based on the width of the div and not the height. This means that i need to know the width to apply the solutions but in my case, i can't do that , since I know the height (100% of the height of the parent) but I don't know the width.

Ive tried to adapt the solution but I was not successful.

Any idea how i can make a 1:1 div knowing the height of the div ?

Thanks !