Tangent is perpendicular to the radius at the point of tangency

Depends on: Perpendicular from a point to a line exists and is unique, Perpendicular segment is shortest.

Statement

Let $\odot O$ be the circle of centre $O$ and radius $R$, let $\ell$ be a tangent to $\odot O$, and let $T$ be the point of tangency (i.e. $\ell \cap \odot O = \{T\}$). Then the radius through the point of tangency is perpendicular to the tangent:

In other words: at the point of tangency, the tangent to a circle is exactly perpendicular to the direction from that point toward the centre.