On a sudden digression or change of course, as in The professor's hard to follow; he's always off on a tangent. This phrase often occurs in the idioms fly off or go off on a tangent, as in The witness was convincing until he went off on a tangent. This expression alludes to the geometric tangent—a line or curve that touches but does not intersect with another line or curve. [Second half of 1700s]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.