Cutting out perfect tangent to circle

it's kind of hard explain i'm going here's crude picture of attempt:

 

 

i want point on circumference of outer circle join horizontally tangent of inner circle - guess top of it.

and want loop round , rejoin; know how cut out once created.

 

 

what's best way create line's orgasmically?

i'm not experienced photoshop / vector work; should using pen tool or shape tools?

do know if hold down shift key while making work path, forces next point horizontal or vertical?

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