$tan \theta = \dfrac{opposite}{adjacent} = opposite$ for $adjacent = r = 1$

Part of calculating the tangent begins with a secant line, defined as a line intersecting the curve in two points. It makes since, given that secant means "to cut or sever" in greek.

But why then, is the trigonometric function named "secant"? I don't see a relationship between $sec \theta = \dfrac{hypotenuse}{adjacent}$ and a secant line.