Sometime my brain works sometimes it's just really slow..
Create the circle at the desired location
Draw two vectors from the center of the circle at the desired angle
Offset each vector the radius of the circle
Clip the unneeded part of the circle and you will have two vectors tangent to the circle
To create tangents to a center point arc draw temporary vector lines at 90° to the desired tangent lines
Create the center point arc
Draw vector lines snapped to arc ends at 90° to temporary vectors