If some straight line touches a circle, and some (other) straight line is joined from the center (of the circle) to the point of contact, then the (straight line) so joined will be perpendicular to the tangent. * For let some straight line $DE$ touch the circle $ABC$ at point $C$, and let the center $F$ of circle $ABC$ have been found [Prop. 3.1], and let $FC$ have been joined from $F$ to $C$. * I say that $FC$ is perpendicular to $DE$.
If a tangent and a radius of a given circle intersect, then they are perpendicular.