How dns rootserver anycast works?

I know the DNS root servers have 13 ips and they use anycast to spread the request to their 800 actual physical servers around the world.

But i do not know how the dns request will target to the nearlest server to my location like HongKong.

And i know the root server in HongKong have a same ip with aother mirror server somewhere, it is legal to have two servers with different physical address in the internet with a same ip?