Creating an arc between two existing arcs

Problem:  You want to create an arc between two existing arcs, such that the new arc is tangent to the other two arcs where their endpoints connect.  This type of problem can occur when preparing a drawing for a CNC program.

Solution #1: This solution guarantees the new arc is tangent to the other two arcs, but it may require moving one of the two existing arcs:
1) Enable OSNAP, Endpoint and Center only.
2) From the Draw menu, select Ray.  Choosing one of the existing arcs, select the arc end point for the ray start point, and select the arc center point for the ray through point.
3) Repeat step 2 for the other existing arc.
4) You now have two rays, and their intersection point is the center point for the new arc. 
5) Enable OSNAP, Endpoint and Intersection only.
6) From the Draw menu, select Arc, Center, Start, End.
7) Choose the ray intersection point for the arc center, and the existing arcs endpoints for the start and end points.
8) If you get almost a full circle, cancel the arc and repeat steps 6 and 7, this time swapping the order you choose the start and end points.
9) You now have a third arc which is exactly tangent to the other two arcs.
10) If the new arc is only connected to one of the pre-existing arcs, you can move the other pre-existing arc so all three are connected, or you can try the second solution below.

Solution #2: This solution is done by eye and guarantees that the arcs are connected. However, the new arc may not be precisely tangent to the other two arcs:
1) Enable OSNAP, Endpoint only (right-click OSNAP status bar button, choose Settings).
2) From the Draw menu, select Arc, Start, End, Direction option.
3) Select the end point of one of the existing arcs for Start, then the start point of the other arc for End.
4) Use the Direction adjustment to adjust the shape of the arc curve so it appears tangent to the other two arcs.  You may be able to see the adjustment more clearly by shrinking the crosshair size to its minimum (Tools menu, Options, Display tab, Crosshair size).