The case is already solved with a tangent drawing extension. Actually in this special case the tangents can be drawn also without that extension. They are as long as the line between the circle midpoints and they can be made by duplicating that connection line. Placing them properly with snapping happens when one draws a 90 degrees rotated copy of the line. Its midpoint snaps to the circle midpoint. In inkscape snap to crossing works well.
The tangents are joined, the resulted rectangle and the circles are combined with Path > Union.
BTW in Inkscape closed areas like circles often cause false snaps if they have a stroke. For that reason it's useful keep them strokeless during the construction.