Basically the Modify->Trim tools are intended for that.
But trimming circles is not always working correct, especially in combination with tangents.
The tolerances in math modules lead to unexpected behavior sometimes.
So to avoid the Trim tool I would divide the circle at the tangent intersections and then delete the desired segment.
To find the tangent intersection you can try Snap intersection mode, but here the tolerances occur too and the Divide tool may not snap to the intersection point.
In this case I add an orthogonal line to the tangent. With the Line->Orthogonal tool select the tangent first and then the center of the circle (use Snap center).
Now you can use the intersection of orthogonal and circle to find the tangent touching point for the Divide tool.
The orthogonal could also be used to trim the tangent correct.
When finished, the orthogonal lines can be deleted for a clean drawing.