on a tangent

(off) on a tangent

suddenly dealing with a completely different matter We were talking about gas prices and you went off on a tangent about your vacation plans.
See also: on, tangent

on a tangent

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]
See also: on, tangent