Let us fly offf on a tangent.

Let Us Fly Off On a Tangent:

To fly off on a tangent, idiomatically, is to digress so radically, such that the topic that one now speaks of is only related to the previous topic – prior to the digression – by having only the point that spurred the tangent in common.

In mathematics, a ‘tangent’ is a line that only has a single point in common with the circumference of a circle.

The tangent line touches[1] the circle’s circumference at a single point, and is perpendicular to the radius of the circle.

The angles that the tangent makes with the radius are right, i.e. of magnitude 90°.

Figure 1: A diagram of a tangent line.

In the circle:

A

, the centre is at point:

a

. The radius of the circle is line segment:

| a b |

. The tangent line is:

| x y |

. The tangent line:

| x y |

, only touches the circle:

A

, at a single point, and that point is point:

b

. The tangent:

| x y |

is perpendicular to the radius:

| a b |

. The angle:

∠xba

is a right angle.

. The angle:

∠yba

is a right angle.

[1]. The Latin participle, ‘tangēns, tangent-, ’ means ‘touching.’ Therefore, etymologically, a tangent line is only touching a circle’s circumference at a single point. The Latin 3^rd-conjugation verb, ‘tangō, tangere, tetigī, tāctum,’ means ‘to touch.’

let_us_fly_off_on_a_tangent