Obviously your arrowed lines snap to the circle. Because Inkscape's arrowheads are beyond the ends of the lines, placing the line ends should be done without snapping. That can seem difficult, but it is possible with the node tool.
Draw the lines as usually. Turn snaps off and with the node tool move the ending nodes of the lines. Have high zoom for accuracy. The result will not be mathematically exact, but it can be accurate enough.
- use arrowless lines + separate arrowhead shapes. Place the arrowhead first. Place then the line. See an example.
- place the lines, scale the circle smaller or have a concentric invisible bigger circle which takes the punches. This is well shown in another case which is suggested in the comments, but I have drawn an example of it, too.
If you convert a line with an arrowhead to path (=Path > Stroke to Path) you get a group which contains the line as filled shape and the arrowhead. Ungroup, remove the stroke from the arrowhead and you have got a freely usable separate arrowhead.
Here the arrowheads have snapped to the red circle. The circles are grouped to keep them together. It's not necessary to delete the red circle. You may need it later. It is inside a group, but it can be selected and closed in the objects panel. That's done in the right.
In the next image the upper arrow is the normal case, the arrow punches the circle. The lower arrowhead is a separate strokeless filled shape, the red curve has been drawn after the arrowhead has been placed.
If the tips of your arrowheads lean perfectly on the circle, they still overlap the circle stroke. You must remove the stroke if it must be an exact fit.