Trim a circle between two tangent lines

What technique can be used to trim a circle between two tangent lines as shown in the figure below?

Note that exploding the circle by using Tools -> Modify -> Explode will not work as the intersection points between the tangent lines and the control points of the circle do not align.

Use Tools - Modify - Divide to cut up the circle at the intersection points with the tangents and then delete the unwanted part of the circle.

Thanks, works great.

Please note, tangent point is always tricky. If it cannot find a tangent point as an intersection, try end points, etc.