Advise on choosing statistical method

Hi. I'm a medicine student and I'm relatively new to statistics. I'm looking at some data and I can not figure out which statistical method I should use.

The setup is the following:

We are investigating disease X on Y number of patients.

Doctor 'A' does a set of 8 clinical tests (I, II, III, IV, V, VI, VII, IIX) on each patient. Each test is either positive or negative (symptom or no symptom)

Then doctor 'B' does a different clinical test (IX) that is either positive or negative.

None of the above mentioned tests are 100% sensitive.

I'm interested in knowing how strong the correlation is between doctor 'A' and doctor 'B's findings. Which method would you recommend using for the above mentioned setup? Any help would be much appreciated. Thank you
Thank you. How do I calculate the significance (i'm not even sure if this is the right term)? I have tried to find an example of how it is done (preferably a step-by-step guide) but I have not found one yet.
I am still a little puzzled. Are you looking at agreement between the doctors? I think not as A and B are not doing the same test. Then why the interest in A vs B; are you not looking for the best test to predict disease?
The proposed methods above are indeed correct for the correlation between all 8 tests and test IX, but I am not sure that is what you are looking for.
Best, Martin