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

Dale