If a function is 'nice' (!), then for every secant line, there is a parallel tangent line!
This is the intuition behind the Mean Value Theorem from Differentiable Calculus.
The fifth problem from I.S.I. B.Stat and B.Math Entrance 2018, has a clever application of this mean value theorem. The first video will tell you more about the theorem. The subsequent videos will expound on its application.