Have ortho on. Draw a vertical line through a point on the edge of your circle. Turn ortho off. Rotate the line around the circle center to the required angle, if any. Extend the line to the required length.
More than one way to mash taters.
Substr
Returns the substring of string , starting at character start and extending for length characters.
$(substr, string, start [, length])
Characters in the string are numbered from 1. If length is omitted, it returns the entire remaining length of the string.
$(substr,$(getvar,"dwgname"),1,10)
Another
osmode 517
Line
pick point on circle "near" etc
pick point "CEN"
Enter
RO L enter end 90
You could make it a pretty simple defun joining all steps.