Sanity Check. DNS Delegation and NS Records? Who is querying who?

Let's say we have a hypothetical DNS server (at 10.10.10.1) with these records and is authoritative for bar.com.

foo.bar.com. IN NS ns1.foo.bar.com. ns1.foo.bar.com. IN A 10.20.20.1 

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We have the other server (at 10.20.20.1) with these records and is authoritative for foo.bar.com

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myhost.foo.bar.com IN A 10.20.20.5 

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If a client queries 10.10.10.1 for myhost.foo.bar.com, does the DNS server 10.10.10.1 query 10.20.20.1 or does the client have to perform two queries...once to get the NS record for foo.bar.com and then a second query to 10.20.20.1 to get the A record for myhost.foo.bar.com?